You tried plugging it into another AC adaptor? The hardware that comes with the device is very specific. If you're going to plug the unit into another power adaptor, make sure that the hardware matches the specifications.
There could be a good deal of things going wrong here. First off, it might not be getting enough power to it, which is why it would be powering down as soon as it boots up. When you initially connected it to your computer, did you get any sort of 'found new hardware' message? Did the device show up in the Disk Management utility?
If at this point it won't stay on then the unit could be dead on arrival. When did you buy it? Where did you buy it from? If you lost your receipt, most retail stores will keep credit card transactions.