On almost every single game I play, GTA 4, Blacklight: Retribution, Tribes Ascend, APB Reloaded, I get 20 fps. But on some games like LoL, WoW, Gotham City Imposters, CSGO, AVA, TF2, I get 60+ Fps. It seems like I have settings set somehow on some games that limits my fps to 20. Even if I go to minimum or maximum settings, it stays at 20 fps. I have looked in the game settings and my computer settings and I am clueless as what I am to do. Any help is much appreciated!

Graphics: AMD Radeon 6520G w/ 512 MB Graphics System Mmemory 2.4 GHz
Processor: AMD Quad-Core Processor A6-3420M
RAM: 4GB DDR3
Windowns 7 64-bit

That setup isn't really ideal for high level gaming. Games that you get 20FPS require far more power than than games like League.

Check with AMD's website and see if there is a new catalyst driver for your APU. If your running a old driver, installing the newest one might free up some more potential.

6520 Graphics is pretty poor for 1080p gaming. You can either lower the resolution in the game or buy a discrete video card like a AMD 7770 or a Nvidia 650 ti. With tomorrow being Black Friday, you can probably snag one for less than $100.
See Here:
http://www.newegg.com/Product/Produc...82E16814127687

If its a pre-built computer, you will also need a 500 watt power supply to run a graphics card.