Although my wifey claimed the problem came and went periodically, it was solid-bad when I got it. Thank goodness!
I popped the cap off the controller box, and could find nothing loose, corroded, or burnt, so I took the plunge, pulled the controller and pried the plastic cover off. Damn hard to get off; but it was just held by little snap-grooves/clips.
Magnifying glasses are great things! It was a cracked run to one end of a resistor. The pad had separated from the trace right where they join (probably thermal), and showed just a bit of messiness on the broken edges -- sort of "folded upwards". It was a big enough crack to be pretty obvious, and that's good because my vision ain't what it used to be.
I scraped off the conformal coating, soldered a wire across the crack, and put some glyptol (stolen fingernail polish from HER) over the joint.
BINGO. Cart runs.
Thanks for all the suggestions, guys.
LLoyd