Hi, I had a similar problem and after visiting the Apple Store, talking to various repairers without progress I concluded it was the power supply or connection. I used some blu-tack to clean the small connector points on both male and female of the Magsafe / MBA and that fixed it. Seems the problem (for me) was just dirt & dust on the connection points that seemed to allow a connection, but not enough to power up or charge. Hope it works for you.