Try taking the battery out and just using the AC Adapter, old batteries can sometimes cause issues. Your description does sound like an overheat issue common with Laptops, are the vents clean on the outside of the Laptop case? They often get clogged with dust. Another very common issue with Laptops is the connection to the motherboard at the AC Adapter point, the AC Adapter cable becomes an intermittent connection because of flex in the cable and breaks the power connection thus shutting off the Laptop or worse the connection at the motherboard becomes bad usually a bad solder joint on the board, so my suggestion is to try an rule out overheating and that was a good attempt you did by removing the Laptop to a cooler position
, next I would try replacing the AC Adapter and see how that goes. If a new AC Adapter fails, then it could be a bad motherboard connection at the AC Adapter point of entry in which case your best option is to take the laptop in for repair.
PS---> Make sure you can hear the Laptop fan spinning up too!
Edited by zep516, 18 August 2012 - 07:01 PM.