Anything in the system logs that give a clue? Start > Run (or ALT + R) and type eventvwr.msc - look in Wndows applications and system logs for any relevant errors or warnings.
A few things to try for a hardware issue (but get a full image backup first as you may kill XP activation by radical hardware changes):
1) Run a good memory tester (Memtest86+ from a boot CD is pretty good) as the symptoms you describe could easily be a memory problem. Let the memory test run for at least a few hours (preferably over night)
2) Try running with only one stick of memory - if you still have a problem try the other stick, try different slots - if Memtest+ didn't flag errors it probably isn't a memory issue but the can be problems with 2 sticks causing issues and Memtest+ isn't 100% perfect because there are small pockets of memory it can't test.
3) Check temperatures are reasonable (after a crash look in the BIOS) - you could try Speedfan which will report temperatures while windows is running
4) Still not found the issue try unplugging all unnecessary hardware from the motherboard: remove 1 memory stick, DVD burner, graphics card if there are onboard graphics that you can use temporarily. Basically remove everything that you can remove and still have a bootable system. Then try running a system stress test (you could use something like SiSoft Sanrda see
http://download.cnet...2086_4-10556571.html) and see if the system still falls over. Again swap and move memory sticks. Once you have a stable system add devices back one at a time and test again.
If you are still having an issue it might be your windows installation. Since you have a full backup of your system wipe your hard disc and install an absolutely minimum version of Windows with minimal hardware and basic drivers wherever possible and stress test again and then add components one at a time and let windows install the drivers it wants where possible. If you get all your hardware back in and can't stress it to fall over and temperatures are OK it was probably your installation that had problems. Then you need to decide whether to struggle to troubleshoot random error problems or just start with a clean installation and extract your data from your backup.