Oh dear rings a bell, windows media player and shutdowns or freezing, happened on my daughters machine after updateing to media player 11, never conclusivly proved it what it was, but i suspected confilcts between software installed to get photos off a phone via a usb connection and media player. Im afraid that the quick solution was taken which was to install another copy of xp on a partion created for the purpose which worked fine with media player 10 and all the rest of the required software including the phone stuff. end result was to delete the orginal xp after moving all the important files i.e. music, photos, homework, email etc.
I guess if possible you could try a rool back of media player or, back to a system restore if you can identify when it started happening. A new xp install was a bit of a heavy handed solution but the quickiest way to resolve things , if it hadn't of worked I would have been looking at hardware as suggested begining with cooling and power supply problems.
The only other place for clues is the event viewer which logs events which take place such as software conflicts but wasnt much use to me on this occasion as whne the shutdown occured it was instant and not logged.
Event view can be found in control panel- administrative tools.
Good luck
Rickity