if with a boot disc it does not work, it is not power setting from the OS. BIOS usually don't have that setting, but it is very possible that it might be an overheating issue. I would start by checking the fans. They are usually a little cumbersome to reach, but they can be reached and replaced on most laptops. I had a desktop to fix once, that the system would not boot because the CPU fan was lose, and it would not even load the POST screen.
Open the laptop, and check if you can turn it on with the fans exposed to see if they turn.