You may want to check the central drive shaft to the rear to make certain the grub screw that holds the cup to the drive axle is actually connected. Those grub screws tend to fall out. What you end up with is a drive shaft that looks functional, but it just free spins when the tranny starts to drive it. If the rear diff seems to be functional, I would check the central drive shaft at the point where it enters the diff. That cup might have lost its grub screw.
Other than that, the only thing I can think of is the within the transmission itself.