The washer won't spin during cycle. The water fills and drains just fine and I can hear the motor working, but there is no spin. How do I fix it?

It sounds like you have a bad motor coupling, but a bad transmission can also give the same kinds of systems. The motor coupling is located between the motor and the transmission.

This is what the part looks like.
http://www.partsdr.com/photos/regular/285753A.jpg