My first entry here said the beep happens during post. That was wrong. It happens before POST.
The sequence of events is:
1) PC freezes, and is completely unresponsive. Only way out is to manually power down. It is now happening during gaming sessions, and it's happening with several different games.
2) When I power up again, it doesn't even go to POST. Just the beeping. BEEEEEEEEP, (pause) BEEEEEEEEEP, (pause) BEEEEEEEEEP. And it will continue beeping until I power down again.
Memory checked out, temp seems fine, card is properly seated (AGP slot hooks are in place). Viruses: no. Spyware: no. Video drivers: not the latest because that requires SP2 and I haven't bothered with that yet. But the problem occurred with my previous card and those drivers were up to date.