Replaced Motherboard, Strange powering on issues.

A customer brought in a MacBook Air that would not turn on. Only thing it did was show the amber light on the MagSafe plug. The customer stated that it showed no signs of failure before it died. He claimed he was using it the night before and in the morning it did nothing. We deemed it a bad motherboard and/or power-jack.

I received the motherboard and replaced the one in the machine. But the only way I can get it to turn on is if I unplug the internal battery, hold down the power button, plug the battery back in, plug in the power adapter and then turn on the machine. After the machine is on I can unplug the power adapter (works on battery fine) and I can use the machine normally. But I cannot power on the machine any other way. I cannot power on the machine without unplugging the battery and holding down the power button. I also replaced the power jack but that didn't seem to make a difference. Any ideas?