Four wheel drive shifter will not move

On the transfer case
Transfer Case - Electronic Shift
The four-wheel drive electronic shift-on-the-fly feature electrically shifts the vehicle transfer case between 2WD, 4WD HIGH, and 4WD LOW. The system mode is selected by the operator through the mode select switch (MSS) on the instrument panel. The operator is informed which mode the system is in by two instrument cluster indicators: one for 4WD HIGH which appears as 4WD, and one for 4WD LOW, which appears as 4WD LOW. Shifts into 4WD HIGH can be made at any speed. When shifting into 4WD HIGH with the vehicle stationary, tooth blockage may occur preventing shift completion. When the vehicle is driven above 8 km/h (5 mph) the shift will complete. When shifting in or out of 4WD LOW, the four-wheel drive (4WD) control module requires that the vehicle speed be less than 5 km/h (3 mph), the brake pedal be applied, and the transmission be in NEUTRAL (automatic transmission) or the clutch pedal be depressed (manual transmission).
The gearmotor encoder assembly is mounted externally on the transfer case. It drives a rotary cam which moves the mode fork and range fork within the transfer case between the 4WD HIGH, 4WD LOW, and 2WD range positions.
The four-wheel drive (4WD) control module controls the gearmotor encoder assembly that shifts between 4WD HIGH, 4WD LOW, and 2WD modes.

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

You can "shift on the fly" at up to 45mph - just let off the gas and pull the shifter back to 4hi. DO NOT try going to 4lo while moving.

Another way is to stop, put it in neutral, and pull the shifter back to 4hi or 4lo.

This is vacuum activated - so if you can't get it to engage - the vacuum motor is failed - or you have a disconnected or rotted vacuum line.

Cherokees have the command - track. You'll see a lever next to the transmission shifter that has letters 2H, 4H, N, 4L on it.
You can shift from 2H (2wheel drive high range) to 4H (4wheel drive high range) at any legal speed.
If it's an automatic, I recommend just taking your feet off of both pedals, so there's not a lot of torque being passed thru the transfer case.
If it's a standard I recommend stepping on the clutch when you shift, but it's not necessary.
To go to Neutral just pull the shifter back one more position to the N position. To shift into 4L (4wheel drive lo range) you must be stopped.
I also recommend shifting the transmission into neutral when you do this. Push the shifter to the right, then pull it back.

Thanks!

full size blazer? if so do you know if you have auto locking hubs on front or manual? the manual will have a dial to turn to lock or free. to shift into 4 high this can be done by just moving the shifter into 4hi at slow speeds. to shift into 4lo need to be in nuetral with vehicle stopped or rolling just a little bit like 1-2mph shift into 4 lo and shift back into drive same when shifting back into 2hi from low range.

Do you have it in neutral? Transmission has to be in neutral to shift into and out of 4 low.

have truck running,,put shifter in neutral,,shift into high lock 4x4,then put truck into gear,,u can shift from high lock to high gear,,from two wheel to four wheel,,in high only,,if u want to shift transfer case in low,,u have to put truck in ,,neutral,,first,,

I've seen some that can be shifted while in park, but generally even when that is possible, it is always better to shift while rolling at a slow speed (under 20mph). When all components are turning, it's easier for them to properly engage without grinding.. If after you are finished using 4x4, the front axle does not disengage, you can usually get it to do so by disengaging the shifter, then backing up for about ten to twenty feet.

go to car wash spray back wheels enough to remove dirt.

Your blazer is equipped with a shift on the fly four wheel drive. That means that at speeds less than fifteen miles per hour you can shift into or out of four wheel drive by simply pushing the four wheel high button. If you wish to shift into four wheel low. Stop, put the transmission into park or neutral, and push the four wheel low button. Same procedure for shifting back out. Never shift into or out of four wheel low while moving. And be careful in four wheel low. At full throttle your still barely moving, you don't want to blow your engine up!

If the Amigo is like other fwd setups,you should be able to pull the floor shifter back one notch for fwd in the standard(or high)driving range.I don't know if you can shift "on the fly" with the Amigo,so I would shift it to 4x4 while stopped in nuetral. When you pull the shifter to the left(towards the driver)and all the way back,that should be 4x4 in the low range(for speeds under 20 mph only). I would not recomend that you drive you vehicle on the highway in low range....The button on the dash may actually be a light to let you know when you are using the fwd. Make sure you kick it back to 2wd when you return on dry pavement.Any Isuzu dealers' service department can also help you on the matter. Good Luck!