Vehicle just stopped when attempting to accelerate and will not Move

My wife was driving our vehicle listed above and she took off from a stop sign and the vehicle started to move then stopped in the middle of the road. It was still running fine but wouldn't budge. A kind older gentleman helped her push it into the nearest parking lot, after watching her put it in gear and seeing the rear drive shaft spin and the vehicle not move he told her the rear end was out. They locked it in 4wd and she drove it the mile to our house. When I had time I jacked it up and took the cover off the rear end to inspect the gears. Other than needing the gear oil changed everything looked fine, no broken teeth or metal shavings. So I took both rear wheels off. While on jack stands I had my wife get in the jeep and crank it up and put it in gear. As she eased off the clutch both rear axles turned and the gears in the reared seemed to turn fine. She shut it off and I spun the driver side axle and the gears in the rear end did not move nor did the passenger side axle. If she spun the passenger axle the driver side would spin (i believe in the opposite direction) I like to try and figure things out myself but I'm working a lot of hours right now and my wife and son would really enjoy being able to ride the vehicle. Looking for any suggestions. I'm no mechanic but I am not afraid to give anything a try with enough instructions.