Well speaking of "arcane",and "those kind of guys" are still around, for clarity see the answer below :)
So what you need to do is open it, remove battery, and clean the mother board and plugs ect.... using NON metallic cleaning objects like toothbrush and q-tip.
Use alcohol (for grease) and Vinegar(or pure lemon juice without sugar) for calk deposits from your spill.
The destinydensity of interconnects is very high and even a small amount of semi-conductive dirt can do what you are experiencing, so give it a good scrub.
Good luck :)