It would be pure speculation to guess what is wrong and you will need to investigate further. Strongly suggest you procure a repair manual if you plan on doing the work yourself. There is a lot of good information and pictures to make the job significantly easier and less expensive in the long run.
Suggest you do a search as others have had engagement issues in the past.
I've included a few pictures on how the 4x4 system works, but did not include the ones for the most recent serial numbers. Hopefully they will provide some value to you.
Please document your findings and resolution, so others can learn.
2012 JD855D OPS Black Poly Roof, Deluxe Cargo Box, Front and Rear Protection, Power Lift, Front Hood Rack, Rear Screen (homemade), 800 Watt Inverter, 2500lb Winch installed in cargo bed, Front and Rear LED auxiliary lighting (4" square 27 watt), Front and Rear CV Guards, Koplin Side Mirrors