Alienware M14x Random/Sudden Shutdown

Hi guys, so I just picked up this laptop about 2 months ago and it's still in great condition. Yesterday, I popped in a DVD and about half an hour into the movie, the laptop suddenly shut down; no weird noises, no weird flashes, no screen of death, just black (off). I turned the computer back on and the windows error recovery screen popped up, so I started windows in normal mode and continued my business. The same thing happened again half an hour later.

When I finished the movie, I put my lid down to put the laptop to sleep, but when I came back later and re-opened the lid, I found my laptop had shut off and I'd get the windows error recovery screen when I turned it back on.

Hours later after (with the DVD still in the drive), the computer suddenly shut down again, and I would get the same windows error recovery screen again. Thinking it was the DVD, I ejected it, but moments later, it happened again.

Today, with a fresh restart and nothing in the disc drive, I put the computer to sleep and the same thing happened again. And throughout the day, the laptop would keep on turning itself off while sleeping.

I've noticed that every time the computer shut down by itself, I've been running on battery, but other than that, I found no other pattern in the random shut downs. And this isn't the first DVD that I've watched on the laptop either.

Do you experts/smart tech ppl have any idea on what's going on?

Here are my specs:

Intel Core i7-2630m
4 GB ram
Nvidia GT 555m; 3 GB video ram
500 GB hdd; 7200 rpm
sound blaster x-fi sound card
1600x900 screen
and everything else is standard config I think.

Thank you guys in advance!