I had the same issue with my MacBook Air with the exact specs, though I never dropped mine. Just shut it off one night after watching Thrones for a few hours and it never turned back. Pleaded with Apple for quite a while to see if they would replace the logic board due to defect, but they did not. Mine was purchased in May 2013 and dead Nov 2014. Finally broke down a couple of years ago and bought a low end I3, with 4gb of ram logic board and it's working again. Guess I would have tried this as well had i known it was an option at the time :)