I'm with James.
Only caveat is that when you rotate one front wheel forward the other should rotate backward, and the driveshaft will not rotate, because all the movement is transmitted by making the opposite wheel rotate the opposite direction.
To get the front driveshaft to rotate you have to rotate both front wheels the same direction.
I kinda forgot that point didn't I..I think you can see Most of the shaft, as they pass thru the Oil pan channel. Of course I don't know what his NH looks like.
Most CUTs have an enclosed driveshaft to the front, so it's gonna be hard to detect rotation anyway.
You never expressed any extreme failure, breakage sounds, abusive use,,, so I'm gonna say it's a simple problem, not necessarily easy to fix. The shifting fork that engages the 4wd may have sheared the roll pin that connects it to the shaft, so engagement of the lever, which rotates the shaft, is not moving the shifting fork. That would mean breaking the tractor open. Not good.
Start with the simplest and easiest thing to fix and work your way up. Good luck and post the results. We are all curious.