Be sure to try with a booster battery when a Vanagon engine will turn over
with the starter but won't fire and run.  The engine computer requires a
higher voltage to function than the starter requires to turn over the
engine.  IIRC the threshold, measured at the battery with the starter
operating, for the ECU to function is about 10.4 volts.  Below that it
just won't start.

From your symptoms this may be the situation.  Once the engine starts, the
battery may charge up enough to function during the day but then the next
morning the cold battery may just not have enough to start.