The washer agitates and drains the water but won’t spin. The motor is working and I have a new belt on, but it won’t spin the drum. I’m thinking it might be the transmission but not sure how to get it out. 
I had the same problem on an older model GE top loader. It ended up being the tube to the level sensor switch. It was partially clogged and the machine wouldn’t go into the spin cycle because the sensor was telling it there was still water in the drum. I was able to take mine loose and blow through it to remove the clog. Total cost: $0.