Alienware x51 random shutdowns - even while using windows restore.

Starting about three months ago, with the occasional random shutdown here and there, my Alienware x51 r2 has become unusable. After countless tries at using the windows repair tool hoping that no random shutdown would occur, of course the pc just decides to shut itself off without warning. Then after the random shutdown, the computer tries to reboot itself. The lights turn on, the fans start but then all of a sudden it beeps and powers off. Then it tries to restart over and over again doing the same thing as described. The only way to get the computer to boot up again is to do a power drain or to unplug everything and leave it for a few hours. This does not solve the problems however, just allows me to boot up the machine. This has only really become a major problem in the last week or so, before that it used to shut down once or twice per day and then usually be fine for the rest of the day. I know this is most likely caused by the small power supply of the x51 or overheating of some sort, but I even took off the case and made sure all the fans were unobstructed etc, but the problem persists.

What must be understood is that I have 5-10 minutes when my computer boots up to do anything. This is not enough time to do a system repair or factory reset, as these usually take up to an hour to complete. In the past, 3 months ago when the problems first started, I used windows to do a factory reset of my system, and this seemed to solve the problem for a while. But now I am extremely lucky if my computer boots into the login screen of windows.

I am wondering if there is any other way to do a factory reset without using windows. I still have all of the discs that the x51 came with. Does anyone have any suggestions to fix these random shutdowns? I am only doing a factory reset because last time I did one the problems seemed to stop for a while.

Any replies are greatly appreciated.