Don't worry about the "Panther" thing or the "kernel power" event. They're not causal - they're side-effects of the problem.
It sounds like the shop is making you jump through hoops for what is very probably a hardware problem. Convincing them may not be easy if they're going to be pig-headed about it. A few suggestions:
1) Try going into the BIOS config menu and staying there for hours if necessary (don't boot into Windows at all). If the same unexplained restart happens while you're in the BIOS, it would really stretch credulity to claim that the cause is anything but hardware.
2) Make sure the BIOS itself is up-to-date. That can sometimes resolve similar symptoms.
3) Test what happens when the OS is reinstalled from scratch and then used without any updates, and without connecting to the internet. Literally no updates, no apps, no games ... nothing that's not on the Windows disc. Painful but potentially necessary as a troubleshooting step.
4) If all that fails to clarify what's going on, I can suggest a method to conclusively determine whether the reboots are caused by software or hardware, though it won't necessarily pinpoint which component in either category is the culprit (it may identify a specific software cause). You'll need another machine close by, and both of them will need to have either firewire (1394) or old-fashioned serial (RS232) ports. It's "last resort" stuff, so I'd suggest you try the other steps first.
Good luck with it.