MacBook Air A1304 Power Problem

I wonder if anyone here can guide me how to repair a power problem in a MacbookAir 2.1 A1304 1,86Ghz.

The problem is that the board isn´t charging the battery and when the magsafe is connected no led in it comes up.

But the board isn´t blown. I can start it if I plug a charged battery (works with battery).

Also it´s not the magsafe connector board since I have tested a different one and it does the same.

Another way that this board starts is if unplug the magsafe, press the power button on the macbook air for a few seconds, leave the power button, plug the magsafe and press the power button again it starts... :S With the fan at maximum speed, but starts. Although working from the magsafe it does´t charge the battery and still no led in the magsafe. But rather than that all works.

So it leaves me to the conclusion that this is a malfunction in the mother board circuit in the battery/power area.

Can anyone guide me on how can I solve this or what component in the board can be causing this? I have some capacity with iron solder and was hopping to repair it myself.