Transmission 2 gear not working

With the engine running and the clutch pressed all the way down try each gear in turn and listen. Do you get any crunching or grinding noises? Nasty noises on gear changes with the clutch fully pressed is commonly a sign of a badly worn clutch. No noises suggests linkage problems or an issue inside the transmission itself.
On a manual transmission you start at the gear stick and work down to the actual transmission. First check the links on the gearstick under the floor. Then follow those cables down to the transmission and check the linkages at that end. Sometimes a worn or loose linkage bush can cause loss of gears. Next check the arms and levers on the outside of the transmission itself. Work it by hand feeling and listening for it "Clunking" as it drops into all the gears. If it doesnt feel solid and 'notchy' the issue could be inside the transmission itself. You'll need a gearbox specialist to look at it for that issue.

This is often times a sign of low transmission fluid or a faulty transmission control solenoid. As you know, automatic transmissions use pressurized hydraulic fluid to change gears or to stop showing 2nd

What are you talking about auto shift control solenoid ? Which transmission does yours have ?
Automatic Transaxle - 3T40 Automatic Transaxle - 4T40-E
1-2 Shift Solenoid Valve
In transmission valve body
Transmission Component Location
Automatic Transmission Internal Connector End Views
2-3 Shift Solenoid Valve
In transmission valve body
Is there a DTC - diagnostic trouble code stored ? Which gear or gears are not working ?

you have blowen the transmission or the belts have snapped

The clutch lining worn out n the lining powder stuck on the transmission filter so transmission fluid pass through the filter clogged.. Only way is to repair the transmission or replace the whole transmission.

it may be your shift solenoids their are two of them that controls upshift #1 solenoid controls 1-2 gears then #2 controls 3-4 which transmission do you have in your suburban do you have the 4L60E OR 4L80E if you have an older suburban with a Carb on it then you will have the 700rr

The gear shift lever indicators tell you what gear you have an automatic transmission in on your vehicle. The shift solenoid tells the transmission when to shift gears and what gear to shift into. Newer model automatic transmissions have electronic shift solenoids that are activated and change gears based on the speed the vehicle is traveling. Troubleshooting either one of these transmission components is relatively easy if you know a little about automobile mechanics. With the right tools, you can determine whether the transmission shift solenoid is having a problem. Gear shift indicator problems can be determined simply by moving the gears into their designated position.
Transmission Shift Solenoid

• 1 Raise each corner of the vehicle up with the car jack and place jack stands under the frame. Make sure the car is raised high enough so you can work under the car freely.
  
• 2 Slide the drain pan under the transmission fluid drain plug. Remove the drain plug with a ratchet and socket, and let all the fluid drain out of the transmission. Remove the transmission pan bolts with a ratchet and socket. Pull the pan away from the bottom of the transmission, revealing the transmission shift solenoid.
  
• 3 Wipe off the shift solenoid with a shop towel. Disconnect one of the two plugs that attaches to the shift solenoid. Turn the knob on the volt meter to the ohms setting, so resistance can be measured. Set the volt meter on 200.
  
• 4 Take the black lead of the volt meter and touch the negative battery terminal wire. Take the red lead of volt meter and slide the tip into the terminal plug you just disconnected from the shift solenoid. Look at the reading you get on the digital display of your volt meter. Determine if the reading is between 12 and 25. Readings below 12 or above 25 tell you that the shift solenoid is not working. Reattach the plug to the shift solenoid and pull the second plug attached to the solenoid. Perform the same procedures on this plug wire. Replace the transmission shift solenoid after determining it is bad.
  

Gear Shift Indicator

• 1 Move the gear shift into the desired gear. Look at the gear labels and the arrow, or other indicator, to see if the gear shift indicator lines up with the selected gear.
  
• 2 Move the gear lever to another gear and look to see if the indicator lines up with the selected gear. Misalignment of the arrow will tell you if there is a problem. Moving the gear shift to "neutral" but having the indicator show the transmission is in "drive" tells you the gear shift indicator is not working properly.
  
• 3 Try each gear position to determine how much misalignment is in the indicator. Slide under the car and check for a loose gear shift cable. Check all the gear shift cable connections to ensure they are all tight and are not missing. Tighten any loose gear shift cable clamps or bolts. Replace the gear shift cable if you find that this is causing the misalignment with the gear shift indicator.
  

Your transmission may need rebuilt. Did you empty the troque converter also? if not do another fluid change as there is still 2-3 quarts of old fluid in there. If it still doesnt work the transmission will need service.

This information is from my genuine service manual. I hope it is of help.
Non-turbo
Turbo
Sedan Wagon
Type 5-forward speeds with synchromesh and 1-reverse
Transmission gear ratio
1st 3.454 3.454
2nd 2.062 1.947
3rd 1.448 1.366
4th 1.088 0.972
5th 0.780 0.738
Reverse 3.333
Front reduction gear Final
Type of gear Hypoid
Gear ratio 4.111 3.900
Rear reduction gear
Transfer
Type of gear Helical
Gear ratio 1.000 1.100
Final
Type of gear Hypoid
Gear ratio 4.111 3.900 3.545
Front differential Type and number of gear Straight bevel gear (Bevel pinion: 2, Bevel gear: 2)
Center differential Type and number of gear
Straight bevel gear
(Bevel pinion: 2, Bevel gear: 2 and viscous coupling)
Transmission gear oil GL-5
Transmission gear oil capacity 3.5 2 (3.7 US qt, 3.1 Imp qt)