The hard drive is a completely separate entity from the "computer" itself, so the fact that the computer turned on and off by itself is a separate issue from the hard drive working or not working... while they may be related in some way, it doesn't help us in troubleshooting the problem, unfortunately. It may be the cause of the hard drive problems, but has nothing to do with the solution.
If the hard drive isn't working, then it's not going to matter whether you're troubleshooting the problem with a Mac or a PC -- the hard drive isn't going to magically "mount" under Windows but fail under Mac OS X. The underlying problem is that the hard drive itself is damaged -- when I say "damaged", I don't mean little nicks or scrapes or holes in the hard drive casing -- I mean that some internal component vital to the operation of the hard drive has failed, and that part may or may not be physically damaged (ie, bent, broken, stuck, etc.) and it may or may not have just ceased working. The hard drive is damaged in a way that prevents it from physically operating.
One trick I used to try was to put my hard drives in an air-tight bag and place them in the freezer for a few hours. Take 'em out, power them on immediately, and salvage data. This worked in cases where a physical, mechanical part of the internals of the hard drive became "stuck" in place (like the read/write arm/head assembly), and the freezing process (as any high school physics student knows!) causes the metals of the hard drive to contract, ever so slightly. This slight movement would sometimes (not all the time) "unstick" the stuck components and the hard drive would work for a short while afterward, letting me get any data off it I could.
I don't think this procedure will work in your case, since even if a mechanical part of the hard drive is stuck, you can't even power on the hard drive anyway, since you have the impression that there's something wrong with the power to the hard drive.
So, I have a possibly dead hard drive in my PC. My mom has some invaluable pictures of a family member who passed away, and they are only on that HD. Is there a way I could use a program on my mac to pull the data off the hard drive? I will buy a fire wire if I must.
Are we troubleshooting the hard drive data recovery issue still, or are we now trying to figure out what's wrong with the computer and why it turns on and off by itself?