Connect the charger that came with the machine to a good power source with not a lot of other items on the same power line from the circuit breaker.
Connect it to the Mac and perform a SMC Reset here and let it charge up for a few hours or overnight before using it.
1. SMC reset
Disconnect other non-Apple and external hardware except (if applicable) a mouse and keyboard until your finished repairing your machine.
Problems solved: Fans blowing with no activity, machine is not booting, power button pressed and nothing happens, problems with indicators, Magsafe has wrong lights, battery is not charging, monitor and graphics issues etc. If the battery is not charged (from like letting it sleep too long), let the Mac charge up awhile afterwards.
Will not hurt the machine resetting if it's not broken.
Other related hardware problems (optional):
Check battery status: Hold option/alt key down while clicking on the battery icon in the menu bar, top right corner.
Magsafe: Use the correct/matching power supply charger with your Mac, not a less powered one from another Mac.
If that doesn't work, please make a appointment with Apple for a repair or evaluation, also if you haven't yet purchased AppleCare you should do so as well as a couple of backup drives.
we got the 3 year extaned for it since its my sisters macbook that she takes to college. I kept telling her for over 2 mouths to back things up the the 2 TB external drive that our imac shares with her laptop as well as my dell so if something like this happend she wouldnt lose every thing. but i told her HDD should be fine though.