Hey Lucas! That charger may actually be your problem. the 85W charger is meant for 15" or 17" macbooks, and they have the batteries to withstand that pressure. Some 13" batteries end up failing after a while due to the excess charging. In conjunction with your magsafe light staying green, it seems that your battery is no longer accepting a charge. :'(
Changing the battery is comically simple, with the only difficulty being some pesky [product|IF145-081-4|Tri-wing screws]. Otherwise you can find a [product|IF163-054|replacement battery here.]
Best of luck with your repair!