Hi Robert and Beth
This is kind of a mystery. I am assuming that your problem exists during both agitate, drain and spin in all cycles.
I suggest you take the motor off and leave it connected and put the machine in spin (you will have to by pass the lid switch) and see if the motor turns. If everything checks out I am leaning towards the capacitor. It is very unusual that they fail, but given your symptoms and what you have already done that seems a logical place to go. If that is not the problem wiring to the motor, the motor connection or the timer would be suspects.
I agree that just changing out parts is not something you want to do, that may be what you have to do in this case.