One possibility -- Check to see if the pins inside the tip of the adapter are all upright. They're pushed up by tiny interior springs -- if they're not all out, they won't make all the necessary connections to power the computer and charge the battery. Flicking the side of the tip can make them pop up. Or maybe you can push them down and see if they'll pop back up with your fingernail.
UPDATE: A shot in the dark -- are you using the original 85w adapter that came with the computer? The 60w adapter from the Macbooks and the 45w adapter from the Macbook Airs will plug into your computer, but may have insufficient power to make everything work properly.
And here's a knowledge-base article from Apple about troubleshooting magsafe adapter problems: http://support.apple.com/kb/TS1713