Went to start the Charger to other day, just a click from the starter. Have tried the following:
Checked battery, even swapped it with another car.
Removed starter, had it checked, still good.
Cleaned all grounds, even added another ground wire from neg. battery cable connector to radiator support.
Cleaned battery connections.
Swapped in spare ignition switch I had kickin around.
Swapped starter relay with other Charger.
With key in crank position voltage at starter relay stud that goes to starter is 11.3. Voltage at starter is 10.75.
Tried jumping across starter relay from stud where battery cable attaches to the stud below.
All the same result, just a click from the starter.

Engine locked up? Put a socket on the crank and see if it turns over freely.

Starter binding?

bad starter

I turned motor over by hand. Forgot to put that in my list.

Replace your battery cables. Both from the battery to the relay, and from the relay to the starter. While your at it, replace the ground cable from the battery to the motor as well. You would be surprised how many battery cables are green inside!

Unless that #4 battery cable is really long, the voltage at the end should be pretty close to the voltage at the start. I've replaced all the small #4 battery cables with an "O" size and have eliminated any voltage drop from my 4' long cables. Gene

don't forget the small wire to the solenoid. i have seen many of those go "green" inside as well, causing the symptom the OP posted.

What I would do now is set a known good battery by the LF wheel & with jumpers run it right to the starter. I would clamp the starter small/large terminals together with one red clamp & the other cable to the starter housing then make the final connection(s) out at the batt & have a helper take hold of the positive clamp on the starter terminals cuz it is close to the starter housing & we dont want it to shift & ground out. this takes everything out of the picture except the starter. EDIT & the motor but we have confirmed that it ain't locked.

Check the ground wire and make sure it is grounded properly.

Its a no carnk issue not a no start.Id also say starter if it just clicks.But Ive seen bad batterys do the same.Had my 65 out and started perfect.Left cruise and no crank.Jumped and got home.Battery at almst 13 volts.Turn on headlights and drops to 1 volt.Battery just went.That and check cables.Ive sen them corrode inside and crate a no crank.But would still show good volts on meter.Just remember a meter can tellyou say 12 volts but not you wont have amps.Rocky

Never mentioned batt voltage. And how was starter checked to be good?

missed this?

With key in crank position voltage at starter relay stud that goes to starter is 11.3. Voltage at starter is 10.75.

I missed that he pulled/checked the starter soooo if the batt is good/charged (& he did change it out) then it has to be (I would think) a voltage drop issue. (& clicking is classic inadequate amperage at the starter) but I got sidetracked cuz I just had a bad starter that just "clicked". It threw me too, I was checking batt/cables all to no avail.

Didn't miss it. OP said Voltage was measured directly at the Relay and starter terminals vs Batt terminals. I know it sounds elementary, but I don't know if both batts will pass a load test.
Also read the starter was removed and checked. Im assuming a starter bench test or was it just physically examined. But if Batts pass load test and the starter was benched tested, then I would look at the cables as RR stated. RR also mentioned testing starter by directly hooking up one of the batts directly to starter. Bypassing the batt cables would be an eliminator. Definitely a frustrating issue.

Starter can test good on floor.But not be good enough to start car.Ive seen it before no load it spins OK.Rocky

In crank mode voltage will drop quite a bit do to the hundreds of amps load the starter puts on the battery. I don't see his measured voltages being out of line, though it would be nice to know the the unloaded battery voltage was to begin with.

Problem really is that most people don't look at this stuff when it's working right so they have no idea what to expect. Leaving them to interpret problems with no basis of comparison.

Would have been nice to have a spare starter. But is this the old original type starter or mini starter? Solenoid could be the issue.

Get someone to tap on the starter as you try to start it.

Update. Got it started. The positive battery cable was cooked. Even with a heat shield around the cables where they pass by the headers the cable still failed.
So a not so funny moment. I change out the cable to a new Y.O. cable- same problem - just a click. So when I double checked all my connections I find that the crimp/connection where the cables tie into the battery terminal were loose and partly pulled out and the crimp was garbage. Pushed the wires back in and crimped it with a set of vice grips and it fired up.

Appreciate all the input and advice.

Good you found the problem. Now does YO owe you an exchange for that bad cable?

One rerason I run at least 1 gauge cables on my 65.Mine have been on decades and still like new.But I dont care if it looks factory.Many do.Rocky