The engine cutting off is a good indicator that something wasn't right with the motor; water in the gas is a definite possibility if they didn't check the fuel prior.

If the engine had continued to run and pull them into the trees, I'd suspect disorientation/vertigo; it's real easy to lose your up/down sense once you start climbing through fog. That's why an instrument rating is nice to have. Was the VFR clearance because they were at an uncontrolled field or weren't IFR certified? Taking off below minimums is a bad idea even if you are rated. If he'd gotten on top of the fog he may have been fine.

The FAA/NTSB report will be interesting. Since they have two eyewitnesses to interview there won't be a lot of guessing.