Here's a tidbit I learned today that I thought I'd pass on:
My laptop wouldn't power up (GASP!!!! ohhhh noooooo!!!!!!). There was no response at all when I pressed the start button, regardless of whether or not it was plugged in.
We took it in to the Best Buy Geek Squad, and the first thing our Geek (sorry, couldn't resist) did was take the battery out. Then he plugged in the laptop, and presto, power.
Apparently sometimes the batteries can move so that one or more of the connectors aren't touching, and rather than allowing the computer to short out, it simply powers down to protect itself (cool huh).
The solution is to make sure that the laptop is turned off, remove the battery, then plug the laptop in using the power cord. Once it's powered up, tip it over and reinsert the battery. At this point you may have to recharge the battery, as it may have become drained (mine was).
Ok DON'T LAUGH. This was news to me!!! I'm a laptop newbie ;-)