Sorry if I wasn't being clear before. My Lisa is a Lisa 2/10 (different CPU board than what you sent me, James). I neglected to put this out there before, but thanks for reminding me.
I've checked the voltages through the widget drive power cable. The -12v connection measures -12.5v, the +12v connection reads +12.3v, and the +5v connection reads +5.2. I think these are all in range.
I looked inside the power supply today, nothing seems out of place or blown at first glance.
Per your request, I've uploaded a short album of pictures here: http://applefrikker.imgur.com/. Hopefully this will help in diagnosis. The trace on the I/O board I was worried about before is photographed, as well as the orange wire I referred to. There are also pictures of the screen when I turn on the Lisa, both the blank one and the one full of random pixels that I said happened once or twice.
Hopefully these pictures will help to narrow down the problem.