I disassembled the entire thing, cleared the CMOS, shook the case around, and put it all back together again. I can only assume that it was a short-circuit that was causing the issue, as my CD drive has an unhelpful habit of shaking its screws loose.

These screws then go on exciting adventures to Das Mutterbord and PSUbervald, liberating masses* of electrons from the restricted paths I lay for them. Order has now been restored, and my will once again goes unchallenged.
...