I'm guessing the adjustment on the one end got forced and after it moves it popped the other end out of the linkage. From your image, the bottom link goes the the transfer-case and the one your holding goes higher up above the one connected and then goes back to the shiftier arm into the cab.
I find sometimes you have to be moving to shift the transfer case, otherwise while stopped possibility the gear is not aligned with where it has to go and will not fall in. Which i believe happened to you, cause you mentioned trying to force it to move.
When it cant move and you force too much on it, it can sometimes push the one linkage thru the adjustment wedge bolt.
That will then make the linkage longer or shorter depending on which way you were forcing it and can then depending on the rubber bushings condition to pop the linkage out of its slot at the other end & depending if you have a body lift or cross member drop with a misaligned linkage.
Check that adjustment area to see if you can see if it has been moved.(usually has rust around it, so easy to spot if it moved sometimes.)
What you can do is to block the front wheels so it cant roll.
May have to jack the rear off the ground slightly. ( so you can try to spin the drive shaft to move the gears if hard to hand shift while under it)
Put the transmission in neutral(engine off).
Try to put the transfer case inside lever into 2 high & crawl under & put the transfer case shift into the 2 high position(all way clockwise).
Then loosen the bolt for the linkage(like pic above) and try to slide it one way or the other to get it to align with the slot it goes into and then press it in.(rust might make it hard to slide)
Then re-tighten the bolt tight.
put transmission in park and start up and try to drive it.
If ever the engine is running and you put in gear and it does not move, DO NOT PUT INTO PARK while engine running after going into a gear if you think the transfer-case maybe in Neutral.
Turn the engine off and then put into park. Otherwise the transmission could be spinning in gear with the engine running(even thou transfercase in neutral) and putting it into park will cause the parking paw to try to lock into a moving part and will make a grinding sound and possibly damage the paw or the drum and put chunks of what broke into the trannys insides and damage it.