Macbook random shutdown

I have the new version of the macbook and for some reason it randomly shuts down when I start it up. However, it runs perfectly when I have the charger plugged in. I had a similar problem before and it ended up being a hardware problem, this was over the summer so i don't think it would happen again. Is there anyway that I can fix this at home? thanks.

Have you tried a new MagSafe Charger Adapter unit? And, if your MacBook is still under warranty or extended Apple care, you may be better off letting Apple look at it.