I'm posting from my own PC, the one in question is actually my brother's. I'm using a PS2 keyboard to interact with it.
Anyway, I gave that a try (I didn't think it would work as the BIOS wasn't seeing them either), but it didn't work. Thanks for the idea though.
One other thing I forgot to mention: The mouse's light does come on, so there's power. The keyboard's backlight comes on and immediately turns off. The thumbdrives I've tried do nothing.