I don't get to work on GE washers a ton, but I once had one that the owner thought the transmission was out. After taking off the front panel, I could see that the motor was working but the clutch wasn't engaging. I replaced the clutch. Have you taken off the front panel to see what's going on? If the belt is slipping and you got a lot of black dusty residue near the belt area, it could just need the belt replaced.