This is what I would do if I were you (I tried to write the steps in order of likelyhood, also as you go along, if you notice anything amiss, google the problem to learn more about it and your possible solutions. Also, bear in mind that it could be some kind of weird, known glitch that you will not be able to figure out using common sense.):
Note: You will most likely not have to complete all of these steps!
1. Disable any screen saver you might have loaded and if there has been any overclocking one on the computer, write down the settings used on a piece of paper, put it in a safe place, then reset the settings to factory defaults in BIOS. Restore the settings if this doesn't solve the problem of if it introduces new ones on top of the old problem.
2. Feel the side of the computer, is it getting hot? If so, go into the bios (or better yet, if your motherboard supports it, run a fan speed/temperature monitoring for your motherboard while windows is in use) and look at the temperatures. Do you hear any whirring noises? Maybe one of the bearings or sleeves has gone bad in one of the key fans. If this is the case, replace the fan. If you have to replace the CPU fan, look into getting some good thermal grease while you're at it to use. (of course, make sure that if you are using thermal grease, you do it properly - research how to do this)
3. If it isn't a heat issue, maybe the RAM is going bad. Download a knoppix live cd (or Mepis, or morphix. Any of these will work). They normally come with a memtest in the boot loader screen. Run this for a few hours to check for errors. Also feel the side of the computer periodically as the test runs. If there are errors, replace the RAM. (Make sure the RAM you buy will be compatible with the motherboard) If there aren't any errors, then run linux for a while. Play some games on it, talk on gAIM, make a few spreadsheets, play some music, whatever. You can also try running windows in safe mode. If it doesn't freeze, then this indicates that there is probably a software, driver, or hard drive problem (if the linux live cd doesn't crash, but windows safe mode does, then your hard drive may be going bad. Listen for some clicking noises). If it does freeze for both a live linux cd AND windows safe mode, skip to step 5. It's probably a hardware problem.
4. If the first two steps haven't solved anything, then perhaps you have a software issue. First, determine if the computer is locking up whenever you have a certain program running in the background. If so, then reinstall that program. If it still gives you problems, uninstall it and forget about it. If there's no rhyme or reason to the lockups, then it's still possible that the CPU, motherboard, graphics card, LAN card, or anything could be going bad, but it's much less likely. Second, I recommend you go to your "Device Manager," and check for any malfunctioning drivers and then reinstall any ones that are. This may sound a bit odd, but I've had this happen before. Then run a thorough virus scan, spyware scans, and a registry cleaner, rebooting as necessary. (I'd recommend using the following free programs: Avast (anti-virus), Spybot - Search & Destroy (anti-spyware), AdAware SE Personal (another anti-spyware), Microsoft Defender (yet another anti-spyware; use all three, because one will catch things that the other won't), and CCleaner (Registry cleaner)). Then run msconfig and in the "startup" tab, disable everything except the essentials, such as anti-virus, firewall, and anti-spyware (if unsure about an entry, google it before disabling it or leaving it enabled!). Also, if you aren't running a firewall, it's possible that some script kiddies have identified your computer as vulnerable and are attacking it. (I recommend using the free version of ZoneAlarm)
5.If your problem still isn't solved, or you are having trouble completing the steps, then it may very well be your hard drive, motherboard, graphics card, or anything else. I've had a few LAN cards go bad, which caused system instability. I've also had a cd-rom go bad, a graphics card, a motherboard, a hard drive.. etc.. The moment I took the offending piece of hardware out, it fixed the problem. Try removing all unnecessary components, such as tv tuners, sound card, firewire reader, LAN cards, etc, etc, then run windows and test it some more. If windows locks up, try safe mode, and then if that locks up the linux live cd (there's no need to run the memtest twice though). If the linux live cd locks up, then proceed to step 6, otherwise, it's probably your hard drive. Use a different hard drive that has an operating system on it on your computer and try to get it working.
6. Find some free computer stress testing utilities (a benchmarking program might work as well, since it will cause your computer to stop working once you start it for whatever the affected component is). Run the test on your Hard Drive, Graphics card, and then CPU. If there are any problems with any of these, the program will either alert you or will lock up shortly after you begin a test (I say to test the hard drive still, because a failing hard drive will sometimes only have problems here and there).
7. This is the last resort, besides buying a new computer or swapping out core components of your system, such as the graphics card, motherboard, or CPU. If the problem still isn't fixed, locate your recovery cds for the computer or your copy of windows. Back up any important data (settings files, mp3s, pictures, game saves, etc, etc), write down what programs you have installed, then format your hard drive, reinstall windows, and reinstall your programs. Be CAREFUL not to accidentally forget not to backup something very important.
8. If you haven't been able to fix the problem or at least diagnose it at this point, then go buy another computer, lol. (or, if you've had some interesting, yet confusing observations while going through this process, contact me and maybe we can brainstorm on the problem.)