Power won't charge battery issue

#1

I have a 13" 2012 MacBook Air. When I plug in the power cable the LED does not light and the battery does not charge. However, if I remove the battery connection from the logic board, the LED lights. When I re attach the battery to the logic board it charges. If I remove the power cable and reattach it, while its charging the LED will not light and the battery will not charge. I've tried changing power cables (with a brand new charge and the problem remains. I've tried to reset the PRAM AND SMC several times and the issue remains. I'm at point where I either try replacing the battery or the logic board.

My thoughts, since the power cord does charge the batteries, the it cannot be a connection issue. Also the USB and headphones work without issue. I have a feeling the issue is simple but I'm not sure. Replacing the battery is cheap but the logic board, is cumbersome as well as $$$.

Any ideas? I appreciate the feedback.

For the record, I let it charge to 100% then I reattached the battery cable. CoconutBattery states that the power is not connected, even though it is...