manic

What are your temps like? Might be getting hot. Is there a hardware
monitor page in bios? There you can look at idle temps, not ideal
but can give you a idea.
Also what kind of voltage are you running, a weak or bad power supply
can cause it to shut down radically as well. If you have no malware
or virus's I doubt a system restore will help, gateway is just trying to
get you off the phone. If its under warranty I would be more aggressive
with them and tell them to fix it.
If you try to replace anything you void the warranty.