My MacBook Air won't charge correctly : the light is green instead of orange
The first thing I would do is an SMC Reset.  According to Apple, one of the reasons to reset your SMC is...



To do a reset


Shut down the Mac.
Plug in the MagSafe or USB-C power adapter to a power source and to your Mac.
Using the built-in keyboard, press Shift Control Option on the left side of the keyboard, then press the power button at the same time.
Release all keys, then press the power button again to turn on your Mac


If you continue to have problems, I would then run an Apple Hardware Test and see if you can obtain any diagnostic info.