Well, when you plug in the AC adapter to charge it.. does a light come on? Most laptops have a little light that tells you it's charging..
If there is a light and its not showing.. then it could be the cord.. or worse scenario, the internal soldering/hardware.
If there is no light and you are unsure.. try running your laptop without the batttery. Just use the AC adapter and see if it'll run. If not, it's probably what I just said above. If it does run.. then it could be the battery.
Since you just got it not too long ago.. maybe take it in for an exchange.. if not, then it could be time for a new battery.