Alienware M14x - Shutting down randomly and having trouble restarting

Hi,

I got my alienware in july and it recently started shutting down randomly. Usually it tries to start up again 2 more times and each time the keyboard lights up but the screen doesn't, then on the last try it beeps 7 times.

I looked it up and according to other sites, 7 beeps means cpu or motherboard failure but my laptop is brand new :(

If I take out my battery and hold the start button then put it back in it has like a 60% chance of starting up again when I try the power button again and everytime I go on my laptop there's like a 40% chance it'll shut down.

And like I said the shut downs appear to be completely random, sometimes I'll be playing a game for >7 hours and nothing will happen, but sometimes I'll be watching a video for 5 mins and it will restart.

My warranty should be only 2 months old, I haven't done any hardware or major software changes to it so my warranty should cover it right?

Please help, I'm in school and I need my laptop working asap,

Thanks.