PC reboots apparently at random - where to start?

[#1]

Hi folks,
I have a PC where the power supply failed, so I put in a new, higher capacity one and decided to rebuild from scratch. It's a bit old now, but fine for XP, with a 2GHz Celeron.
I also increased the memory to 512MB as it had only 384 before.
All went fine for a few days, brought it up to date (SP3) and installed a few apps, AVG and Defender etc.
But now it just randomly reboots, sometimes after hours but sometimes it has a "burst" of several in a few seconds until the BIOS halts with an error on lost CPU speed settings.
Windows knows nothing about it, no complaints at all after the reboot.
So, where to start? Any suggestions anyone?
I'm currently running the Windows Memory Diagnostics (from bootable CD) which hasn't so far shown any errors (though there has been a crash-reboot or two!).
That final point suggests it's not Windows-related but basic hardware of some sort.

[#2]

Sounds as if the bios is getting corrupt which would suggest windows is writing to the wrong memory area. Is there a bios update available? Clear thee cmos by removing the battery for a short while

[#3]

The part which puzzles me is that Windows doesn't want to run checkdisk after the reboot which tends to indicate that Windows is happy with the reboot. Could it be an XP initiated restart.

[#4]

I think I know what it is, thanks for your comments.
Almost certainly the power supply, maybe a dry joint inside on the AC side.
I just happened to move the power cable a little and it rebooted.
Trying a little gentle manipulation, even with the lead pushed firmly in, produced the same effect with total repeatability.
And yes, I did try several other cables just in case 

[#5]

FYI the windows memory tester is pretty useless at finding memory problems. Use memtest86 or the slightly better memtest86+ which will run from a bootable floppy or CD.