I replaced the coupler on my washer which would not spin nor agitate. Now when i try to start it, the motor just hums, and that's all. The transmission and motor shafts both turned freely when I had it apart. Do I need a new motor, or are there other possibilities?

THAT, my friend, qualifies you as a real appliance tech! I think every one of us "experts" has done something like that before. The real pros just never tell their wives! Congrats on fixing your washer.