Further experimentation shows it's definitely problems in the electronics in the K301 itself. Here's what I've got now:
- The "Menu" button on the K301 no longer does anything.
- The "Source" button no longer changes sources, but every 3rd push enables the touchscreen (and the following push disables it again).
- None of the utilities in TouchKit work any more. (They all die at "Reading Parameters from Controller")
In short, it looks like the K301's embedded microprocessor has lost its mind.