We waited way longer than we should have, as we always do, because repairmen are usually expensive. But finally, we got one out this morning. He looked for a few seconds, then said, "did you know your dishwasher is on a switch? This light switch here turns the power on and off to the dishwasher, and it's turned off."
So, we've been living without a dishwasher for months, and even bought a whole new one which wasn't cheap, because the switch that didn't seem to do anything had turned our dishwasher's power off.