I, personally, have never had any problems with Norton antivirus alone. It's usually when a customer has the full Norton suite when i see problems. McAfee has caused me severe personal trauma through the years...
Your problem is tough to diagnose because you said "(it doesnt seem to do this if AH is running)".
If it were heat or power supply problems it would definitely crash during AH. Also any background task would tend to 'upset' the computer while playing AH. It's not going into standby or something right? Your actually using the computer and then the screen goes black?