It turns out the reason the computer had a finicky power supply was that the connection between the power plug (which enters the hole in the bottom left of this picture) and the motherboard (green thing) was weakened by excessive heat. Essentially, the factory solder that made that connection had melted and broken. So I re-soldered the little metal rectangle you can see in the lower left back onto the motherboard. I didn't do a very good job - I'm out of practice. The voltmeter is there reading 0.00 to symbolically indicate the deadness of the computer before I re-soldered it.