I suspect similar to what ratsarsse has said.
XP now by default allows you to restart after stop error, where as before (in NT) you would just have the blue screen of death. The only way around this was to restart manually.
In this situation the power supply was not a suspect as you would see it all happen and know the software crashed (yes maybe because of faulty memory).
However, with auto reboot it looks like it could be a power problem...
Before replacing the power supply, find the option and switch of auto reboot, if you start getting blue screens then it's software.
I have this very problem on a 2 month old laptop, it still has the suppliers software build on it which normally I never leave, I like to wipe the disk and install everything myself, that way I know it's good, and what's on it.
However, I know it's software because when I run a little app at start up to shut down all the background processes, the problem never occurs, when I don't I'm restarting 1-2 times every hour!
There's a couple of free apps, kill it all, or the one I use End It All (recommended as a way to speed up flight sim performance). It's great, no more re-starts! I have about 22 processes running of which I only keep about 5 up after I run it. I don't notice a performance increase but then it's a good spec laptop that I don't challenge too much.
Just rememeber to not allow it to close your anti virus or firewall software.
Hope this helps
Cheers