Memory can cause all kinds of problems, from random rebooting to what your post has discribed. I also have seen IRQ and IO hardware conflicts produce the same type of thing. At this point its hard to say what the computer problem could be.
One other thought, maybe one of the Win XP services is not restarting correctly. You might try going to
www.blackviper.com and go thought the list of services on your computer and disabling the services that you don't need. That might help out your computer at the cost of lossing some of the extra WinXP features.