I'm currently having exactly the same issue with a Hotpoint (made by GE, I believe). I pulled the front panel to see what was going on. During spin, (with the door switch cheated) the motor runs fine (can see the motor shaft turning at full speed), but the belt pulley it is attached to does not move, and gets hot. Belt is fine, not loose. I believe the problem is in the clutch, which is connected to the belt pulley. I plan to replace my clutch after pulling it off and inspecting it for obvious damage or looseness.

By the way, it seems to agitate fine, and it drains fine, as it has a separate motor for the drain pump. Good luck with yours - hope it's nothing major.