MacBook Air not charging when powered off

My Mac has worked fine for 2 years. No issues. Now, it will no longer charge when powered off. However, when powered on it charges like a champ. Also, while powered on and plugged in all operations work fine but when I unplug the power cable the internal fan ramps up and runs none stop and the computer get sluggish. It used to not do this... I have wiped my machine and started it form scratch thinking this would fix the problem, but it did not. Any Ideas?