sounds like cpu overheating, using heavy programs and it shutting down and taking 15 min to start back up??
when this happens and u press the power button what dsoe it do just do nothing? cause thats what happend to me once my cpu fan got unplugged by accident and my cpu went up to 91 C lol when i press the power button nothing would happen, it was scary untill i fent the heat radiating from my head sink lol