We have been experiencing the very same problem.
As mentioned in Yeti's answer, we checked the out of balance switch ,which is very easy to get to.
It had Gunked up and was in the closed position. You can easily tell as the small protrusion which is the actual switch, wasn't protruding very far.
So I worked it a few times and it came back to life which you can tell by feeling it clicking.
It'll probably do it again, but for now, we can wash our clothes again.
I'm very impressed with how easy it is to get into these units and quickly service them. It's given us years of good service.
But if you do decide to venture into the insides of any device, make sure you are careful and remember how it was before you pulled it apart.
Cheers
Tim
Tim Brownlaw, April 2009