Why does my computer freeze and then get stuck with a blinking white underscore?

Markery

Distinguished
Jul 15, 2011
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This is a problem that I've literally been trying to figure out for 2 years, but have procrastinated it due to not having the money to buy new components, and it works 95% of the time. I custom built a computer about 3 years ago for about $500.

I have a 500W Cooler Master power supply
AsRock motherboard
4GB of RAM
A dual core processor
Windows 8
(I can probably find specific details if requested)

It ran fine for the longest time, until I started having problems with it completely freezing up while I'm playing games or something, requiring a force shut down. This has gotten progressively worse, freezing on more simple tasks like web browsing now. It does a really distinct set of things once a freeze occurs. Firstly, I can try to start it right after, but I get no response from my monitor at all, though the fans and everything power up. I always have to wait at least 10 minutes before it interact with the monitor. After that, it beeps once, shows me the ASRock motherboard logo, then gets stuck on a black screen with a white underscore blinking forever until I force stop it. Sometimes it will take a while. Usually I have to try it, wait, try it, wait, etc, like 15-20 times and like an hours before finally it will give me the "Windows has shut down incorrectly" and I can start it normally with no problems and use it until it freezes again (usually a week or so).

I'm just looking for some advice, because I'm not sure where to start. One thing that happens is whenever I finally get it started, some of my files on my desktop end up on the far left when they weren't before. Also, I've taken off the fan and heatsink on the CPU numerous times to clean without scraping or reapplying any thermal grease, which might result in overheating and the freezing. But I'm not sure, and I don't really have the money to experiment with new parts that may or may not solve my problem. Any advice?