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