Chosen Solution
The video chip is toast on my Mac Book. The problem is that year’s video chips all have the same defect. Can I put a logic board in, say from 2013, and get a functioning, non defect machine. Yes my laptop from 2011 was still functioning very well until this past week.
You would have to stay with the A1286 model series. You may be able to use the 2012 board but the 2013 are all Retina machines. Hang on and let me do a little research on the 2012 board, it may have display cable length issues. @danj says you can do it here: Can I replace the logic board with MacBook Pro 15" Unibody Mid 2012? Meanwhile have you tried just turning off the dual graphics using something like gfxCardStatus https://gfx.io I have saved several of the 2011 15” machines using this.
I don’t know for sure, but I would doubt that you can transfer pieces between models. Apple builds all their devices so that you can’t do that, so I would assume that there is some safeguard they put in place against doing this.
