After doing some googling, unfortunately I think the problem might be with the motherboard. It's an ASUS p4800-e and I've seen people talk about the same problem with that line of motherboard. If so, it could be because the 9600 didn't use a power cable and taxed the system harder than the 1300, which did use a power cable. The 7600GT uses a power cable but it presumably requires more power than the 1300, so the problem manifested itself after installing that card.
Whatever.. I'm screwed I think, regardless. I guess I'll take it into a local repair shop.