Maybe try various troubleshooting techniques first. Maybe shut down Norton then try and run Premier, or try shutting down several tasks and try again. Maybe even try and boot in safe mode and attempt to make it crash.
Try and rule out software before you blame hardware, because software conflicts are a ton easier to fix than hardware issues. And, if were a hardware issue i would assume that you would be experiencing a lot more problems than the one you described.
Also Norton... Well Norton sucks. Correct me if I'm wrong, but i can't stand that program.
Good advice and I will follow-up on your suggestions.