That doesn't look like corrosion. It looks more like mold or fungus. Either way, the way to clean it up is to use the highest purity isopropyl (rubbing) alcohol you can find and a short-bristled brush. Drop a few drops of alcohol on the spot, scrub it carefully with the brush, then rinse it off with more alcohol. Continue until the discoloration is gone, then rinse a few more times (toward the left side of the computer). This may not fix the computer. It's possible that there is more gunk on the other side of the logic board. But at least you'll have cleande up this part, and I think things should be a lot better.
By the way, that looks like the result of something organic (soda, wine, etc.) being just slightly dripped through the keyboard. This kind of thing happens, but it's almost always curable.
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