Chosen Solution
A piece of plastic melted on our dishwasher (66515113K216) heating element, and within a few weeks the heating element failed at that spot. We ran it for a few more months before I ordered the replacement part. Once installed, the new heating element didn’t work. I can’t imagine multiple things failed at once, unless the fault in the old heating element may have “blown” something else. I replaced the high limit thermostat as it seemed like the most likely culprit, but no joy. Before I go and replace every part in this dang thing, I’d like to apply a method to my madness. I do have a multimeter, and both new parts seem to conduct just fine (as does the original high limit thermostat, dangit). Thanks!
It was a simple fix, and I probably wasted my money by buying the high limit thermostat. I needed to reset the machine by running the diagnostic cycle. Just pick any three buttons and label them 1, 2, and 3 in your mind, then hit 1-2-3-1-2-3-1-2-3 with less than 1 second between presses. This runs a relatively short diagnostic cycle, and the heating element began working again immediately thereafter.