Transmission won't move?

Yes, the transfer case can be stuck in neutral, can I ask if the transmission grinds when you put it in park? This would be a sign something is broken or in neutral after the transmission. Do you have any codes? I would run the PCM to see if any are stored, here is a guide to help

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

To manually shift the transfer case you will need to remove the encoder, (shift motor) here is the location. Also, if you leave the wiring on the encoder you can work the controls to see if it moves. Check out the images (below). Please let us know what happens.

Yes it grinds when putting in park. I will check the encoder motor like u said.

What would happen if the rear end gears are 342 but they are supposed to be 373?

If is grinds in park without the vehicle moving it means the transfer case is in neutral or the transfer case is broken internally. If you have to two different differential gear ratios it will end up breaking the transferase if you drive in 4x4. So if this is the case I would install a used transfer case and not use 4x4. If you want to have 4x4 you will need to change out the rear end for the correct ratio gears or change the gear set to get the correct ratio.

The encoder motor works. We put transfer case back in and hooked everything up. Still no movement. If it is the wrong transfer case, will this happen? Or do I have to relearn it to the truck?

You should not have to relearn anything for the tuck to move. Something must be broken inside the transfer case. On level ground, I would lift the rear end up and while in park try to rotate the rear driveshaft, it should not turn and if it does the transfer case will need to come out and be rebuilt.