Same problem, green light on the Magsafe connector, no charge. However, before that happened I had a Magsafe connector fail at the strain relief, so I bought a 3rd party power supply from Amazon that had a detachable cable, plus an extra cable. I cut the cable on the 2012 Macbook Air 13” power supply, and spliced in the new cable. It worked for another year, then the Magsafe end started showing green and not charging. I used the Amazon power supply with it’s cable and it worked fine. My 2014 Macbook Pro 13” power supply also worked fine on the Air. So I think my problem is not in the logic board. I am suspecting the pins in the Magsafe connector.