Kernel panics?
You have an 820-2850 board. There are issues inside the vias in the board on these models. Some theorize it is an issue with pgood signal for VRAM dropping, some theorize it is LVDS_MUX issues inside the PCB. There are mods people have proposed to make the pgood signal more stable but they don't work. I've tried my own, no difference.
I think it's just a pile of junk. Apple knows it. http://support.apple.com/en-us/HT203554
With other models you can replace the GPU and it works, with this board it really is just unfixable. Even the replacement Apple will give you under that program will not work properly.
I take pride in fixing all of the issues that other people say are unfixable, but I know my limits. When it comes to the 820-2850 board inside of 15" A1286 2010 models, it's time to give up. Unfortunately that machine belongs in the bin. :(