Clicks but won't crank

Hello to all, I'm hoping to find an answer to a VERY frustrating issue.

A couple of days ago, my sons 94 3.8 mustang which we are both direly in need of, wouldn't start when we came out of Walmart. Turn the key and we get a good strong click, but no crank. Tried a jump from another driver, same thing. we were able to push start (clutch start) it and get home, ran fine, no power loss, bright lights, etc. Did also try a jump with a portable jump starter freshly charged. Same click. Battery terminals all clean, grounds look good too, cleaned and tight. Starter solenoid is on the starter, took starter out and had it tested. Machine says it passed and it did push out the post and spin but there was bright sparks each time it engaged. Wasn't sure what to make of that so replaced it anyway. Same click, replaced relay, same click. Volt meter says 12.23v on battery, 12.55 on portable jump battery.

Click is good and loud, almost sounds like metal on metal but no whine as if starter is spinning. Continuity seems good, got a beep between motor and body. There does not seem to be a second solenoid anywhere.

I'm getting stumped, any ideas? Any ideas on how to test/troubleshoot and get some more rule outs, or ins for that matter. I'm pretty savvy, but no mechanic. You might have to explain a term here and there, but I'm all ears.

Had an idea, I took my jumper cables, connected one end of the neg cable to the metal starter body itself and the other to the neg battery post. Thus bypassing ANY other grounds and got the same click.

Turned on the lights and tried starting, they reacted but only slightly, still quite white. I think I can get my volt meter in to test the voltage at the starter so I will try that in a bit. (Snowing)

If I tried getting my positive cable connected to the starter without first removing the hot battery cable, would that cause a problem or would it tell me anything?

Also, managed to get my volt meter into the hot lead. I didn't have a good solid touch but read up to 11.7 something v, tomorrow I'll make a jump wire and alligator clip it to the hot lead, that should give me a good connect.

So, if its still a little under 12v, might that be the issue or would it at least crank? I'm also wondering about the lead just being too old, would that make it resist the current?

K, looks like I got it. I alligator clipped a jumper wire to the battery cable at the starter. noticed that it was fluctuating between 11.90v and 12.0v. So I started going over connections again, this time cutting off electrical tape wraps and heat shrink plastic as I went.

I found these connections 3-4 inches from the battery post connections, they looked like some big lead weights with a screw in them. They had been heat shrink covered but the plastic had deteriorated somewhat. I unscrewed the connection and cleaned the cable which didn't really look corroded or anything, then re tightened them. I guess I remade the connection cuz the car fired right up. Did it a couple of times, got my fingers crossed.