Computer keeps crashing and freezing

Hi, my computer keeps crashing and freezing every time I play games (mostly from Steam but not limited to) that use some level of advanced graphics, so Skyrim, Guild Wars 2, Minecraft etc. If it does not cause my computer to crash after a while, it makes the program close, sometimes suddenly and without notice, or even causes these small pixels that constantly move to appear on my screen.

I have tried programs that look for minidumps and registry errors, and I have updated my drivers. I have a Hp pavilion p6367c-b with a nvidia GeForce GT 220 graphics card , Windows 7, and I'm not really sure what else to write. This has been happening for a while now, about a few months, so some help would be appreciated :)

This is what the pixels look like btw. Pixels.png
 
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