2002 V6 mustang wont start, changed so many parts, at a loss

My 2002 V6 mustang won't start. It began right after I got home and now it just clicks a single time (starter).

I started troubleshooting by checking the starter relay & fuse, replacing them with no luck. Then I tested the battery myself and it read 12.4V with the car off, not bad but this could be due to my failed attempts to start the car. I brung the old battery to get tested at an autozone and they just told me there COULD be a bad cell, so I bought a new battery anyway, the old one was at least 4 years old.

New battery, car still wont start. The alternator is also less than 6 months old and the brake lamp switch was replaced about 4 months ago. New battery reads 12.6V when off.

Finally, we replaced the starter with a new one. Both autozones in my area said their starter testers didn't work. Car still did not start

Used a continuity tester on the fuses, all checked out and the starter was put in properly.

Motor ran like a dream and is in pristine condition for its age as stated by blackstone labs.

What in god's name is going on?

Battery terminals are clean, grounds look fine, and me and my friends are dumbfounded.
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