My Christine

thread moved

When it doesn't start, what does it do? Does it not crank at all?

You may have some kind of parasitic drain on the battery, or it's also possible that either the starter or the starter solenoid are on their way out. Cables are not a bad thing to change, hopefully that will help.

When you're jumping across the solenoid, are you jumping from battery + direct to the starter (thick wire to thick wire), or from battery + to the thin ignition trigger wire on the solenoid? You don't mention changing the solenoid, those are very often faulty. The fact that the solenoid is clicking means it's getting voltage from the ignition (so a new lock, ignition switch, and push button won't help), but it's not getting the power to the starter.

To get the engine to start, you should be able to turn over the key (doesn't need to be in start position, but in 'run'), and jump from battery + to the little lead on the solenoid. If that isn't working, your solenoid is bad, or the cable from solenoid to starter, or finally the starter itself. (Assuming the battery is good and charged).