When plugged in laptop overheats and dies.

I have a custom built laptop from ibuypower.com It's about 2.5 years old and I've been running it pretty much as a PC since the screen broke. (I've kept it plugged it almost constantly for about a year and a half). Recently, when I plug the power chord in and start a program, after about 10 minutes the fan kicks on to full and after about an hour or two of this it dies on me. I opened the back and cleaned the fan, so it isn't an issue with ventilation, but it is surely an overheating issue, I'm just not sure what. Any help would be appreciated.