Steve, it is possible that this is caused by a bad lid switch. The lid switch has to be closed for the drain and spin cycle to work. If the lid switch is not working properly, your washer will still fill and wash, but that's it. Jump the switch and see if that resolves it. Here is a video that shows you how to replace the switch. Also, make sure that your machine is draining properly, clean the coin trap by the pump from any debris etc.
Other possibilities are of course the motor, bad timer switches, and a broken cam driver. None of these of course sound like fun. "There is also a chance that it is your transmission. Take a look on here for an excellent description. You can download a service manual from here.It will show you how to do the repair as well as the function of the parts. Here is a good video about working on your washer. I do hope that this will help you out. Good Luck.
I've had the coupler that goes between the motor & the transmission fail twice before. The center opening that slides on the motor shaft rounds out, especially if it is overloaded (lots of wet towels is my wife's favorite trick). The replacement part has a metal insert to help strengthen the hole in the coupler.
There are several videos on-line that show how to replace it. Here is one: http://www.youtube.com/watch?v=nM4DW2bq7...