I don't want to talk anyones' heads off here, so I'm going to give very straightforward details, and hope for the best.

I have an Alienware Aurora R4, which I got about 2.5 years ago. It's worked great, up until these recent storms in my area (Quite a bit of thunderstorms in the past few days). I came home today to find my computer off. I usually turn it off, but I didn't today since I'd only be out a few hours. I figured it was a Windows Update that shut my computer down, but it wasn't. My computer wouldn't turn on at all. 

I tried unplugging it and holding the power button down for 30-45 seconds, and plugging the computer back in. This is where I got my best response. The computer turned on (Automatically, I didn't have to press the power button) for about 3 seconds, then turned off. After this, the computer wouldn't turn on at all. An hour later I tried the same method, unplugging it, holding down the power button, and plugging it back in. It turned off after about 3 seconds this time as well.

I also tried the power supply test button, and the power supply works. My only explanation at this point is the weather messed with it. 

I'm looking for any tips/advice at all towards the problem. A big chunk of my lifestyle relies on the computer, and any response at all is extremely appreciated. Also, would my "Complete Care" warranty be able to cover this? I have that for another few months, thankfully.