Sometimes these problems can be caused by a bad driver or other software. XP has an excellent feature that allows you to roll back your system state to a prior point without affecting your data.
To see how to use the System Restore feature, visit:
http://www.microsoft.com/windowsxp/u...emrestore.mspx
(Do not confuse this with a Restore CD that may have come with your system, for that WILL remove your data.)
While I've never seen random reboots caused by not having enough RAM, I have seen defective RAM cause these kind of problems.
Microsoft has a very good bootable memory diagnostics that will help determine if your memory is defective.
http://oca.microsoft.com/en/windiag.asp