why will my vehicle start only if I jump across the solenoid

Without knowing the entire back story on this and without being able to hands-on test components, we can only guess that you have a concern with something from the ignition cylinder to the ignition electrical switch to the electrical connections that allow the starter to engage -- including relays and even the MLP sensor (manual level position sensor) also know as the neutral safety switch or transmission range sensor. It's going to take a wiring diagram, voltmeter / ohmmeter tester, and patience to dig in and figure out the failure.