Dosh, check out this post I made regarding the Dell Inspiron 5150's (5100 is 99.9% similar with a different power connector).
http://www.mp3car.com/vbulletin/showthread.php?t=88036
I have a contact at Dell, that could help you out, and get the board replaced for free (possibly). You have to PM me though to get the info, and promise never give out his info to the general public (I don't want him ****ed at me).
Alternatively, you could call them multiple times until you get a helpful tech that will listen to your problem.
It's only covered if you didn't spill or do anything like drop it to damage the board... they have power supply problems, charging problems and heating problems.