Transfer will not shift out of low range

Does placing it in neutral put the entire drive in neutral???? Yes . Taking the vehicle to a qualified repair shop that has a factory or professional scan tool to read code's in the transfer case control module is what you should do , you probably have no clue of the complexity of these 4X4 systems . How many buttons on the switch on the instrument panel ?
The BW 4493/4494 transfer case features a 4-button shift control switch (1) located on the instrument panel. When the vehicle has the ignition key in the RUN position, the transfer case shift control module starts monitoring the transfer case shift control switch to determine if the driver desires a new mode/gear position. At a single press of the transfer case shift control switch, the lamp of the new desired position begins flashing to inform the driver that the transfer case shift control module has received the request for a new mode/gear position. The lamp continues to flash until all shifting criteria have been met and the new mode/gear position has been reached, or has been engaged. Once the new mode/gear position is fully active, the switch indicator lamp for the new position remains ON constantly.

During normal driving situations, the transfer case operates in the 4HI mode. When the 4HI mode is selected, the transfer case shift control module sends 12-volts to an electrical motor, which is the transfer case encoder motor. This motor rotates the transfer case shift detent lever shaft which moves the shift forks and range sleeve to obtain different modes/ranges.
The BW 4493/4494 transfer case has the added feature of also providing the driver with 3 manual mode/range positions:
• 4HI - 4-Wheel Drive High Open
• 4HI Lock - 4-Wheel Drive High Locked
• 4LO Lock - 4-Wheel Drive Low Locked
The driver may choose to select any of these mode/range positions while driving the vehicle. However, the transfer case will not allow a shift into or out of 4LO Lock unless the following criteria has been met:

DTC B0790 Transfer Case Neutral Indicator Circuit Malfunction
DTC B2725 ATC Mode Switch Circuit Malfunction
The mode switch circuit consists of 5 modes. The transfer case shift control module supplies a regulated 5 volts, DC to the switch through the 5-volt regulator circuit. The current travels through the resistor of the currently pressed mode button. The current is then returned to the transfer case shift control module through the switch signal circuit.
The transfer case shift control module constantly monitors this signal voltage to determine the condition of the mode switch circuit.
When each of the modes are selected they will complete a circuit through their own specific resistor while the button is pressed. The transfer case shift control module continuously monitors the switch input to determine whether the Neutral, Differential Lock, 4HI, 4HI Lock, or 4LO Lock mode was selected by the driver.

DTC C0306 Motor A or B Circuit Malfunction
The transfer case motor is a bi-directional, permanent magnet, D.C. motor. When energized, through motor control A or motor control B, the ground is provided by the opposing motor control circuit and then grounded through the transfer case shift control module ground circuit, the motor, through a series of gears, rotates a shaft which moves the mode and range forks to shift the transfer case between the following ranges:
• 4HI
• 4HI Lock
• 4LO Lock
• Neutral
This DTC detects an open, short to voltage, or short to ground in the motor control A or motor control B circuits, or an open, or short to ground inside the motor.

DTC C0327 Encoder Circuit Malfunction
DTC C0329
DTC C0359
DTC C0550

The Borg Warner (BW) model 4493/4494 NR4 transfer case is a 2-speed, full-time 4WD, transfer case. The transfer case has an external planetary type differential, which has 2 different sets of pinion gears. The planetary differential provides a 40/60 torque split front/rear full-time. This means the front and rear propeller shafts are constantly being driven for maximum traction in all conditions. A high/low planetary carrier assembly provides the high and low ranges, which is a 6-pinion gear, sun gear, and annulus gear arrangement, giving a 2.64 low range reduction ratio in the BW 4493 and a 4:1 ratio in the BW 4494.

You have a switch on the instrument panel ?
The NVG 263 transfer case features a three button shift control switch located on the instrument panel
The NVG 236/246 transfer case features a 4 button shift control switch located on the instrument panel.
Or
The New Venture Gear (NVG) 261, RPO NP2 transfer case is a two-speed, part-time with "mode shift-on-the-fly" capability. It has a chain driven front output shaft and an epicyclical low range planetary arrangement. The NVG 261 transfer case features a four position shift lever control located in the vehicle floor plan. As required, the operator can select 4HI position from 2HI "on-the-fly," as described in the owners manual. A dash 4WD lamp will continue flashing during shifting, until all criteria have been met and the new mode/range position has been reached. Once the new mode/range position is fully engaged and the front axle disconnect locks in, the dash light 4WD indicator lamp will remain ON constantly. Range shifting functions similarly, although it should be limited to speeds 8 km/h (5 mph) or less.

Before trying to replace the switch ,are any lights flashing ? 2hi , 4lo, 4hi etc... Do you know which transfer case yours has ?
Transfer Case - BW 4482-NR4
Transfer Case - NVG 246-NP8
How many buttons ?
The BW 4482 transfer case features a 3-button shift control switch located on the instrument panel.
The NVG 246 EAU transfer case features a 4 button shift control switch located on the instrument panel
Before you replace the switch and finding out that it isn't the problem . The switch is a low voltage input to the tansfer case shift control module (A COMPUTER ) Could have diagnostic trouble codes stored .
DTC B0790
DTC B2725
DTC C0306
DTC C0327
DTC C0329
DTC C0359
DTC C0550
Auto part stores can not read these codes .

The BW 4482 transfer case features a 3-button shift control switch located on the instrument panel. When the vehicle has the ignition key in the RUN position, the transfer case shift control module starts monitoring the transfer case shift control switch to determine if the driver desires a new mode/range position. At a single press of the transfer case shift control switch, the lamp of the new desired position will begin flashing to inform the driver that the transfer case shift control module has received the request for a new mode/range position. The lamp will continue to flash until all shifting criteria have been met and the new mode/range position has been reached, or has been engaged. Once the new mode/range position is fully active, the switch indicator lamp for the new position will remain ON constantly. In addition, the switch includes a VSES request button which sends a voltage signal to the transfer case shift control module. The transfer case shift control module in turn sends a request via the class 2 data bus to the ABS control module which controls the VSES system.

The NVG 246 EAU transfer case features a 4 button shift control switch located on the instrument panel. When the ignition key is in the RUN position, the transfer case shift control module monitors the transfer case shift control switch to determine if the driver desires a new mode/range position. At a single press of the transfer case shift control switch, the lamp of the new desired position will begin flashing to inform the driver that the transfer case shift control module has received the request for a new mode/range position. The lamp will continue to flash until all shifting criteria has been met and the new mode/range position has been reached, or has been engaged. Once the new mode/range position is fully active, the switch indicator lamp for the new position will remain ON constantly.
DTC B2725
Circuit Description
The range/mode switch circuit consists of 5 modes. The transfer case shift control module supplies 5 volts to the switch through the 5 volt reference circuit. The current travel through the resistor of the currently active mode. The current is then returned to the transfer case shift control module through the switch signal circuit.
The transfer case shift control module constantly monitors this signal voltage to determine the condition of the mode switch circuit.
When each of the modes are selected they complete a circuit through their own specific resistor. The transfer case shift control module continuously monitors the switch input to determine whether the Neutral, AWD, 2HI, 4HI, or 4LO mode was selected by the driver.

You may want to take this to a repair shop .

did you turn the locks on the wheels, or check the fuses

Which do you have ?
Transfer Case - NVG 236 (Two Speed Automatic)
Transfer Case - NVG 233-NP1 (Two Speed Selectable)
The NV236 transfer case is an automatic transfer case with three drive ranges. Shifting from rear wheel drive to four wheel drive is done automatically when the transfer case shift control module receives wheel rotating slip information from the speed sensors. The transfer case shift control module then engages the transfer case motor/encoder to position the transfer case from rear to four wheel drive. When the transfer case shift control module receives information that the wheel rotation is the same on both axles, the transfer case shift control module sends position information to the motor/encoder to put the transfer case back into rear wheel drive. The three drive ranges are 2HI, 4HI, and 4LO. The 2HI position is for normal driving with the rear wheels pushing the vehicle. The 4HI, position is for driving through sand, snow, mud, gravel, or heavy rain at normal or slightly below normal speeds. The 4HI engages the front axle to allow for four wheel drive. The front axle is pulling the vehicle, and the rear axle is pushing the vehicle. The 4LO range is used for off road driving, heavy snow, deep mud, or shallow fording. The 4LO is similar to the 4HI except that the gearing in the transfer case is set for low speed and high torque. The NV236 is manufactured at Syracuse New York by New Venture Gear a division of New Process Gear for General Motors.
Is the switch light on or flashing ? If you have automatic 4x4 there are several DTC'S that can set >
DTC B2725 ATC Mode Switch Circuit Malfunction DTC C0300 Rear Speed Sensor Malfunction DTC C0305 Front Speed Sensor Malfunction DTC C0308 Motor A/B Circuit Low DTC C0309 Motor A/B Circuit High DTC C0310 Motor A/B Circuit Open DTC C0315 Motor Ground Circuit Open DTC C0323 T-Case Lock Circuit Low DTC C0324 T-Case Lock Circuit High DTC C0327 Encoder Circuit Malfunction DTC C0362 4LO Discrete Output Circuit High DTC C0367 Front Axle Control Circuit High DTC C0374 General System Malfunction DTC C0376 Front/Rear Shaft Speed Mismatch DTC C0387 Unable to Perform Shift DTC C0550 ECU Malfunction DTC C0611 VIN Information Error

Is the transfer case in High or Low range? If there are no codes present I would almost suspect that the transfer case is in Low range, because of those shift speeds.

1. • 1 Start your Dodge truck's engine.
     
   • 2 Turn the electronic transfer case from "2WD" to "4WD Lock" to engage the high range 4WD, if the dodge truck is equipped with an electronic transfer case; otherwise, shift the transfer case lever from "2H" to "4H." The electronic transfer case is located on the instrument panel and is marked with "2WD," "4WD Lock" and 4WD Low." The lever-equipped transfer case is located to the right of your leg and is marked with "2H," "4H" and "4L."
     
   • 3 Shift the transmission into "Neutral" while the vehicle is either stopped or rolling at 2 to 3 mph to begin engaging in the low range 4WD. Turn the electronic transfer case to "4WD Low," if the Dodge truck is equipped with an electronic transfer case; otherwise, shift the transfer case lever from "2H" or "4H" to "4L."
     
   Tips & Warnings
   • Indicator lights will come on and alert you that your vehicle is in either the high or low range of 4WD.
     
   • Do not engage in the low range of 4WD drive if the transmission is in gear; you must shift to "Neutral" first.
     
   • Many Dodge trucks allow you to shift from 2-wheel drive to the high range of 4WD at up to 55 mph--consult your truck's manual to ensure that this is possible. Do not exceed 55 mph while engaged in the high range of 4WD. Do not exceed 25 mph while engaged in the low range of 4WD.
     
   • Do not engage in 4WD unless you are on slipper or rocky roads.
     

The transfer case is stuck in the low range. If manual shift try shifting from low to high several times to see if free up. If electronic, check all fuses and make sure you hear transfer case change range. Do this by shifting with key on engine off. If no change refer to qualified transmission mechanic.

try putting your truck in neutral and then shifting into 2 wheel drive shift on the fly does not apply to 4 low only 4 high and on electric shift models it wont shift unless your ****** is in neutral.