Hello Notyetbreathing,
There are several reasons that causes a computer to crash.
The first thing I would do is keep hitting F8 during startup to access the boot menu. When it comes up, hit disable automatic reboot during system failure. What that will do
is prevent the computer from just automatically rebooting and it will show you the blue screen associated with the crash. If you do get a blue screen to show up, post what it says and I can take a look at it.
The next thing you can do is run a memory diagnostic and hard drive diagnostic. You can click my Memtest link to download Memtest for free. Also, if you find out the manufacturer of your hard drive, you can go to their website and download a free diagnostic tool. Both tools will let you create a boot disk that you can boot to and run a diagnostic which will test the stability of your memory and hard drive.
If both of those come up clean and you never find a blue screen, then the next thing I would do is try to get my hands on a power supply and video card to test with. If you buy each from a retailer like Best Buy, you can use it for 30 days and return both if you choose to. See if changing those out helps. Make sure you thoroughly test each by itself. Don't change both at the same time cause then you won't know which one helped if you get your computer working right.
Hope that helps! Let me know what you come up with.
