How to clean DUST stucked due to moisture on pins of chips ICs of motherboard circuits
See the grunge on the parts next to the BGA chip under the heatsink?



There will be similar grunge under the BGA chip, between the balls.  The only way that will work reliably again is to remove the chip, clean the pads, re-ball the BGA, and reinstall it.

That's going to be a difficult task.  If you can't do that, there's no point in cleaning up the rest of the board.

If you can't remove, re-ball, and reinstall BGA parts, then this board is scrap.



That "grunge" is corrosion.  

It causes poor connections in places where you should have good connections.

It also causes poor connections in places where you should have no connections.