I'd like to revisit this issue... I ordered the door latch assembly and replaced it this morning. No change in the symptoms. More info: I set it on normal wash and press start. It shows me "56" minutes on the display, makes a quiet buzz for about a half second, then blinks "PAU" in the display alternating with "56". If I press start again, it does the same thing -- short buzz then alternates "PAU" and "56".
When I repeated the original process, which was setting it on spin/drain and pressing start, I get the same symptoms as before. It shows "13" and clicks a couple times. If I let it sit it will eventually count down to "12" and click some more. No water, no spinning, no activity at all.
A note on the door latch: When I ordered the latch, they told me I would need a wiring harness and strike plate. I assumed that was because the latch was a compatible replacement but not the original, and that the connectors on the latch would be different than the connectors on my existing wiring harness. When I removed the latch mechanism, however, I found the existing connectors matched my new latch just fine so I did not replace the wiring harness (nor the strike plate, which also matched mine exactly). It seems to me that it wouldn't be likely that a wire would fail and more likely that the latch would fail.
I hesitate to open the wiring harness and try it just to see if it works because it is the most expensive part of the whole job ($130) and I can return it if I don't open it.
Any further suggestions before we go buy a new washer?