Will not start, clicking, replaced battery and starter

Clicking at the starter or at a relay elsewhere?

The Medic

Of course, nobody likes hearing this.

Recheck the connections, really look at the connections to the battery (while they are disconnected) see if they are green. On side posts you can sort of peel the rubber from around the lollipops and scrub them good on both sides with a wire brush. Then roll it back on around them.

I am suggesting this because you said it sometimes will crank, temperature and humidity will play tricks on corrosion.

I have to throw this out there too, even a new part can be bad right off of the shelf (battery or starter). I received four new (but bad) ignition modules in a row from a parts store a few years back.

If you 'move" the crank (really the flywheel) a 1/4 turn using a ratchet or a wrench (with key off), does the ball game change when you go to start it?

See picture below of me moving my 1977 Jeep CJ-5 crankshaft with a wrench.

The Medic

As The Medic suggests, check all connections. It sounds like either a bad ground or power feed. If the solenoid is clicking it is getting some power, but not enough to crank the starter.