It's Alive! ALIVE!

I'm not satisfied with this--Oh, no! I need this Game Boy to be portable once again, so I used my trusty tri-wing screwdriver to open up the case and see how much corrosion was inside. The following picture is not for the feint of heart.

As you can see, the corrosion is pretty bad. It looks like that copper shielding is being eaten away. On the top board, there's a lot of corrosion around a cap labeled "C6".
So how do I clean up all this corrosion? Should I replace that C6 cap? I don't really know anything about soldering, but this board doesn't look too dense. There seems to be lots of room for error. Is there any specific metal cleaner I should use for this project?

