You've got so much going on, that it's hard to point fingers.
Based on the "Backstory", I'd say that overheating compromised the head gasket as the head warped and that much of what you're seeing is the result. You can test the fan - from what I remember, there are only two pins on its connector. If it's a brushless DC motor that drives the fan blades, you'll need to observe polarity. Figure out from wiring diagrams which is the negative terminal, and with a little creativity, you can use your battery to test it. |