I know this is a dead thread, but maybe someone is listening...
I have exactly the same problem with my Alienware Area-51 M9750 laptop - random power down - instant shutdown with no warning.
This has only happened twice during the last couple of weeks. Last night it happened again and again and again. This time, I removed the cover to check the graphics cards, CPU, memory etc. I removed both hard drives completely, removed the memory, and repositioned the memory, and removed the battery. With the memory removed, the PC was powering up then shutting down then powering up again by itself, etc. I don't know whether that's usual or not. There were no beeps from the POST at any stage, I'm not sure if portables have a beeper or not.
The PC was powering up and then a few seconds later powering down again. Sometimes it didn't even get through the POST. Sometimes it happened when sitting idle in the BIOS screens. Sometimes I was able to get part way through booting Vista or Linux. Mostly, it was instant shutdown a few seconds after power-up. Today, the PC has been on all day, and only shutdown once about 1/2 hour ago.
The graphics cards are cool, the CPU is cool, Fans are working, and memory checks out fine with memtest 86+.
I was beginning to suspect a faulty power switch, but I'm doubting that now because it is so random.
The battery is fully charged, and the power supply is OK as far as I can tell.
Any help would be appreciated.