I actually have already solved the problem, which I guess I should have posted.
The problem I was having was that the washer tub would not spin, but the motor would make a buzzing noise. After finding a Youtube video showing how to remove the front cover of a GE washer (the one in the video looked very similar to the Hotpoint I was working on, so I guessed there was a relationship), I popped the front cover off to find a fibrous material (sound deadener, I guess) wrapped around the drive pulley under the tub and on the motor. Removing as much of the material as possible fixed the problem, at the expense of a bit more noise.
Thanks for the manual link. I'll keep it in case another problem comes up.