Are you quite sure that the logic board was properly cleaned? The goo is surprisingly stubborn, and a light soak and swish might not suffice. You might want to have a good look at the logic board in bright light, preferably with a magnifying glass, checking around the surface mount chips. If you have residual goo, you have your problem: the current would then be going everywhere in general rather than somewhere in particular.
I have brushed around the goo (lightly) under running water with a soft toothbrush and had good results — most recently on an 840av, but also on a Classic II. Rubbing alcohol and a Q-tip also seems to do the trick.

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