Your problem could very well be the result of the Norton 2002 installation. Various users have had similar problems with XP from other anti virus packages.
I would suggest going to the Norton Website, or better yet giving their tech support a call, after all you have paid for it as part of your new program, and see if they have any specific solution or patch. Even though you have a new package there maybe patches that update it, very common cause who knows when the box was made.
There are other things that can cause the problem and might not become noticed or happen until a change is made to the system, like a software install.
One program that has been particularly bothersome is the Roxio Easy CD Creator, and there are fixes attheir web site.
What is actually happening is that XP is running into a error condition, which is set by default to protect the system by a reboot. But the message about the error might either be turned off, or happening so fast you don't get a chance to see it.
If you are the detective type you might consider looking at the following, To check why your system had a failure, check the Event logs for any error messages. You can find the Event Viewer in the Administrative Tools, or by typing eventvwr in the Open box from the Run command.
Another suggestion has been to turn the automatic reboot action off. CAUTION, this is not a long term solution and should only be used until you can determine other possible causes. To make the change, This behavior can be changed by going to the System applet in Control Panel, select the Advanced tab and click the Settings button under the Startup and Recovery heading. Under System failure, un-check Automatically restart.