Bugs, bugs, and more bugs. All of the "this can't ever have worked" variety. Of course they only showed up after I committed the changes, so they inconvenienced everyone instead of just me. Bleah.
Had to stop work abruptly when the power-supply fan began emitting hideous grinding noises. I have the worst luck with fans... As it was 7PM on a Saturday, I had no option but to attempt to repair the thing myself. Fortunately, if you don't mind ignoring the stickers on the outside of the PSU:
OPENING WILL VOID YOUR WARRANTY
TURN BACK NOW, FOOL!
it is quite straightforward to extract the fan from the power supply, dismantle it, and clean out the grit which causes the hideous grinding noise. The worst part of the whole exercise was figuring out how to test it. ATX power supplies don't turn on when you flip the switch, you have to plug them back into the motherboard and push the software on button. (Presumably it's possible to put a jumper across some pins in the big fat connector, instead, but they don't label them.) Don't plug the hard drives back in, or it will try to boot.
I'm paranoid, so I pulled everything off the motherboard before testing: CPU, memory, ribbon cables, video card, etc. But I didn't unplug the speaker. The chipset noticed it didn't have a CPU and started beeping angrily. Scared the cat out of the room.
How does grit get in the fan bearings, you ask? Being as how my computer sits on the floor, which is covered with gritty dust, which the fan sucks into the computer, I'm surprised it didn't happen earlier. I wonder if you can get air filters for a computer case.