Okay, I pulled out the power supply and checked it with my voltmeter. One of the pins is supplying +5V trickle power. With the drives out, I reinserted the power supply and figured I'd give it a try. When I push the power key on the keyboard, the LED on the motherboard blinks and will continue to do so as long as the power key is held down. But it won't come up.

A jumper is present at W1. There is an empty SIMM slot just to the left of the power supply. I don't see any evidence of leaking capacitors, but do these symptoms say otherwise? I wonder if it's grounding out somewhere. Thoughts?