Have you tried washing the logic board? Seriously. Stick it in a dishwasher if possible (only it, obviously, with no soap), wash, remove, and let it dry in a warm, ventilated place. It'll maybe take a couple of days to dry thoroughly. You can scarcely make things worse than they are.

Alternatively, in Conquests someone recently got a CC logic board. You might be able to persuade that fellow member to part with it.