Susan, Josh is a great guy to talk to. I never did manage to get the bean chute for my k6 that's shattered into 12 pieces though... I digress
Are you getting a hum from the motor or just an electrical hum. Can you shoot a quick video?
If you feel daring....
With the bottom off and beans out, lay it on the side with the on off switch up, pin the thing down with a foot or small child, then tap each connector with something wooden, like a popsicle stick. When you hit one that causes it to fire up unplug the k10, then unplug and replug the plug. Look for burns inside, that'll be the sparking of a loose connection. Also look for degraded metal, should be fairly shiny, and not look like aluminum that's been boiled. The caps could be a problem but they don't show bulging. Something tells me it's going to be up top where the problem is. If I remember mine right the switch should glow, orange. Does it flicker or go out when it won't run?
I never took my 10 apart so this is the first internals I've seen of it.