Do some searching over at http://www.feoa.net to see if you can find
any answers there.

You might have a leaky fuel injector that allows fuel into one cylinder,
flooding it, and also allowing the pressure in the system to drop. Leaving
the key on without starting the engine allows the fuel pump to bring the
pressure up. Usually the fuel pump only runs a few seconds if the engine
doesn't start, so I don't see why it must be exactly 10 seconds. You can
test this by turning the key on several times for only 3-4 seconds in order
to build up pressure. (You normally do this after changing a fuel filter.)

Holding the gas pedal to the floor while cranking will temporarily shut
off the injectors while cranking the engine, in order to clear a flooded
engine.

Bob