Burnt wires

What you're looking at is (a blurry iPhone picture of) a white wire from the source and a white wire from the dishwasher -- both of which have about four inches of insulation burnt off them -- and the wire nut that had connected the two, which is now burnt through. Below is the wire nut that had connected the two blacks; it's also burnt, presumably by the white from the source resting against it.

No wonder the dishwasher wouldn't work!

The dishwasher works now, thanks to handyman Dan, but we're going to have to get somebody who actually knows something to take a look at this thing and figure out why the wires burnt out in the first place.