The good news is that the dishwasher is still under full warranty, that I got a real person in this country on the phone, after pressing only one menu option (schedule service), and that I can have a repair visit on Monday. Wow.
Well, and the bottom rack is still working, so that's something anyway. :)
And now to find something to entertain me while I scrub the counters and wash a large amount of dishes.
Update Minor Roadblock: I can't find the purchase receipt, and the serial number is oldish. I called Lowe's, and they said that the store should be able to reprint the receipt for me. I called the store and found out that they will be open tomorrow, so we'll stop on the way to the airport.