1996 Jeep transmission problems

I can not move in reverse. I can jack up the Jeep and put it in neutral and turn the wheels forward but not backwards. It drives fine forward, but just can't back up. Any ideas.

Sounds more like rear end problems to me. I mean even in neutral it doesn't go backwards. I guess there is one way to tell though. Take the drive shaft off and then try to turn the tires backwards. If they still don't turn you have a definite rear problem. You're probably looking at a rear end rebuild or you could just buy a new one and put it in. But check just in case.