Odd starting problem

If that pump keeps clicking fast it might be because of low
voltage. It can't get full travel, since it causes a voltage drop and
the solenoid releases before it has taken in fuel and so won't build
fuel pressure. The engine's refusal to crank is another indication of
electrical problem.
Dirty battery terminals. Corroded cable terminals, where
they're crimped to the wire. An old, worn master solenoid and probably
starter solenoid, too. If the battery is fully charged and it still
won't crank, you need to start measuring voltage drops across terminals
and solenoids while attempting to crank.

Dan

He already explained jumping the airplane battery from a car.

He already explained jumping the airplane battery from a car.

That makes absolutely no difference if the master or starter
solenoids are defective, or if cable crimps are corroded. All that
amperage can't reach the starter if there are bad connections
elsewhere. We regularly find bad solenoids in older airplanes, and the
only way to fix it is to either start replacing them, or getting smart
and checking voltage drops across them while cranking. The copper
contacts in them oxidize with age, even in low-time airplanes, and will
be burned in higher-time aircraft. It only takes a fraction of an ohm
to stop things.

Dan