So I got a newer power supply (one that was in a computer that was barely used), figured out how to get it out. Took the power supply that I figured wasn't working in the problem computer... only to realize that the two power supplies are different so I can't even hook the other one up to the problem computer to try it. I put the power supply back in the problem computer for now, and it powers up so I didn't ruin it. Now I'm confident that when I get the right power supply I'll be able to switch them. It'll be a few days now before I can post an update to see if that will work. In the mean time, anyone else have any ideas?