I was getting impatient with 'em when they kept giving me the same diagnosis. They told me on the phone that they were getting ready to format the drives and reinstall Windows when I told 'em not to lay another finger on the machine and that I'd be there right away.
They gave me a clue when they said that it only restarted when IE was running. I got it home and everything seemed to be working, loading email, Trillian connecting, etc. It was only blowing up sporadically on IE, too. If I loaded a text-only piece of HTML, it was rock-steady, but when I want to my homepage (www.iwon.com), it'd blow up. Figuring it was a plugin, I uninstalled every plugin I could find, but to no avail. I then thought it might be one of the two plugins that seem to be impossible to uninstall, Flash Player or Java. On a lark, I went to the one website that I knew would not contain any flash content, and it loaded just fine. I then went to the one site that I was certain would contain Flash content, and it immediately rebooted.
I searched Google for a way to uninstall the Flash player and found this. After downloading the utility and uninstalling, everything worked wonderfully. I then re-installed the Flash player, and everything was fine.
I can only assume that something odd got written to the disk when we got the "power event" last week, and my Flash player was left in an odd state that would reboot the machine whenever it was run.