Update

Well, reinstalling the media center drivers and their associated paraphernalia did the trick (it seems my helpful help desk employee actually deleted a video card driver, which is a strange thing to do in the service of making the computer start up faster). But from now on, no one from work touches my PC. I think I'll reinstall the HP help, too (which he deleted with the verbal flourish, "You don't need them now, you have us").

And thanks to HP, which actually puts all these reinstallation and troubleshooting tools where a novice (read, moron) like myself can find them, even under the influence of rage at having my leisure time stolen and even at 2 in the morning.