Latitude E5520 will not power up.

Hi all,

I've been having a problem with my Latitude E5520.  The other day, my girlfriend was using it, finished what she was doing, and put the computer to sleep.  Later on, I went to use it, and it was completely dead in the water.  No lights or anything when I went to power it up.  What's most concerning to me is when I plug the charger in, the blue light on the charger turns of as soon as I plug it in to the computer.  I'm thinking it might be a combination of a dead battery and a dead charging board.  I've done a bit of looking and it doesn't seem like this is a common problem, so I guess I'm just looking for a bit of guidance.