Check BJB ( aka Battery Junction Box, Engine Compartment fuse panel ) Fuse #17. This is the power to the Transfer
Case shift relay, which powers the Shift motor in the Transfer case and power to the magnetic clutch coil ( via the transfer case relay ).
The other fuse to check is the CJB ( aka Central Junction Box, cab fuse panel ) Fuse #23.
If both fuses check good, time to check for power on the connector for the shift relay and the shift motor. The power from BJB Fuse # 17 is the Dark Green w/ Light Green stripe ( this is hot at all times ).
The old school test is to lightly hit the back of the transfer case, to see if the shift motor is hung up.
Here are the diagrams, so you can see what I am talking about.