"Replaced the latch switches for $48 without bothering to check them for faults"
"The control board does appear to have a burnt spot but I can't be bothered to tell anyone whether that is near a component, nor what the component is"
"should I spend more money in getting that board with a core charge?"
Why not do some proper diagnostics?
Check this page, there is a link for an electrical diagram, so you can spend a while playing "chase the volts" and actually have a chance to see where power isn't getting through.
There is always the chance of a cracked track or a failed solder joint on the pcb - both eminently fixable..