MacBook Pro A1278 won't work on ac adapter?

I have a macbook pro A1278 unibody and when you plug in the adapter to it no green light or no charging light, and it does not charge at all. It does however turn on if you plug in a charged battery. I have tried 2 different magsafe boards on the logic board and same issue. Tried few different adapters. Another funny thing is that if you have the adapter plugged in and the battery plugged in and you turn it on then unplug the battery while it is on, then it will stay powered on. This macbook has never been dropped, no water damage. Some help would be appreciated. Thanks.