So I had the same problem only the machine (Macbook a1342) did not at all want to start.
Magsafe stayed green.
I replace the DC board and voila, the Macbook was back to live and magsafe light was orange. Charging went well and soon got on 20%
To see what would happen, I decided to unplug the magsafe from the machine while having the charger in the outlet. That I plugged the magsafe back onto the machine and I heard and saw a sparkle. Now the light states green but the charge seems normal. I am afraid the DC board is damaged again somehow and wonder why. The charger has the correct value 60W a1344 for the Macbook a1342.