thank you for your question hope this helps.
It's either one of 2 things.. It's either the v ac switch on the side of the transfer case, or the encoder motor...I would lean more towards the encoder motor.
there have been means owners with this same problem.
here is how i would go repairing this problem
1. Raise vehicle safely so that you have enough room to work under the drivers side. Always use jack stands or another suitable support for your vehicle.2. Locate the encoder motor, it will be right next to the front drive shaft yoke on the transfer case. (You will notice a round plastic dust cover going sideways under the transmission)3. Have an assistant press the 4x4 button so you can listen to see if the motor even moves or if it possibly shifts the transfer case into gear, or you may hear no sound at all, motor dead.4. removed the front drive shaft for additional room. This thing is in there tight, little or no room to work. Remember to mark your drive shaft for proper re installation with a grease pen etc.5. be careful so that your bearing caps don't fall off the U joints unless your gonna to replace them.6. Use a 10mm wrench to loosen and remove the very top bolt holding in the encoder motor. Its way on top and hard to see. you should be able to remove the other two with a socket wrench. (3 in all)7. To remove the motor pushed the encoder motor farthest away from the transfer case as possible but it still wouldn't come off, but almost. Then used a large screwdriver or pry bar and preyed it forward, VERY GENTLY. If you can remove the front yoke from the transfer case you should have no problems at all.8. It pop's forward and out. Then have an assistant press the 4x4 button once more while your watching the gear inside the encoder motor. It was fidgeting back and forth so you knew immediately something in not right inside.9. Remove the wiring harness with an 8mm socket and take the motor to the bench. (no sense in laying on the ground working on it) 10. Remove the torx screws that hold the case together and pried it apart, it is pretty gummed together and there are pry points. I would recommend using the pry points as the case isnt the strongest thing ever made.11. Inside you will notice the gear coming off the motor was cracked in two but still in place, but no chance of it effectively engaging the transfer case.
Blue= Wiring Harness Connector
Blue= Torx case screws
Gear Assembly-Broken main gear
Broken Main Gear-How it is supposed to look.
i hope this helps you