For a while now I have been experiencing problems with my computer, namely when I have it on for a very long time (1 whole day) or I run a large program (League of legends), both my monitors will go black and the computer will still be running. When I try to type on the keyboard nothing happens and the num-lock key does not turn off the light. The only way to get the screens to come back on and the computer to be "unfrozen" is to manually turn of the computer by holding the power button.I have looked this up and what Ive learned is that it may either be a fried motherboard, or graphics card. I was wondering if anyone in this forum would be able to give their insight onto what might be causing this because It is very annoying when I cant use my computer for games that I need it for.

Definitely sounds like your graphics card might be busted, or the drivers aren't working correctly.

Try updating your graphics card drivers, and if that doesn't work, consider getting a new graphics card.

A fried motherboard sounds a bit unlikely as that would probably impact more, most likely not letting you even turn on the computer, but it's hard to tell.

It could just be overheating. Try taking the panel off your computer case and blowing a fan at it and see if the problem still occurs.

Sounds most like an overheat, next like a driver problem. Could be the video card, the processor, or even the northbridge/southbridge chipset.

As Alyxx and Ross said, driver updates and side panel removal. (unless it's a laptop, then just stick a fan underneath it)

I experienced this exact issue when my HD4850 was overheating due to the fact it was slowly dying and becoming unable to keep its temperature low when under strain. It would usually die when it reached 100 degrees Celsius.

Try running this utility and let us know how you get on:

http://www.ozone3d.net/benchmarks/fur/

It defiantly sounds like a hardware issue if it's freezing that severely.