This looks like a faulty graphics chip on the logic board. You have 3 options to repair this:
* 1- Replace the entire logic board.
* 2- Perform a reflow on the faulty graphics chip with a heat gun. Check out this old post: [http://www.ifixit.com/Answers/View/18484/video+graphics+and+boot+issues]
* 3- What i have done that works best is to perform a BGA reballing on the graphics chip but you need specialized tools and skills with soldering to do this and can be more expensive than replacing the logic board
What I would do in your situation is attempt the reflow first to see if it works. If it doesn't then I would just replace the logic board. See this guide: [guide|895]
If you want more info on reflowing or reballing try a google search of GPU reflow diy, BGA rework.
I hope this helps, good luck!