Shifting is electronically controlled and if the motor is not working, it could be a fault with the control module etc.
See if you can get any trouble codes and proceed from there.
RETRIEVING DIAGNOSTIC TROUBLE CODES
NOTE: DTCs are displayed on 3 transfer case shift select buttons. When proper conditions are met, select buttons will blink to indicate DTC from "1" to "4".
1. Turn ignition off for at least 6 seconds. Locate DLC near right side of steering column. Install jumper wire between ground and diagnostic pigtail terminal No. 13 (Orange wire) at DLC.
2. Turn ignition on, engine off. Observe shift select buttons. If all shift select buttons blink once at same time then stop, no DTCs are stored. If only one DTCs is stored, DTC will blink repeatedly with a 3 second delay between sequences. If more than one DTC is present, next DTC will flash after a 3 second delay, then sequence will repeat. Count number of blinks for each DTC.
3. Record all DTCs. After retrieving DTCs, clear TCCM memory and repeat procedure. If DTCs return, perform appropriate DTC test.
CLEARING DIAGNOSTIC TROUBLE CODES
Turn ignition off. Remove 4WD fuse No. 15 (15-amp). Wait at least 40 seconds and reinstall fuse. Cycle ignition on and off 5 times. All DTCs will be cleared from TCCM memory.