Starter wont engage
At this point, I'd do as advised earlier ---- clip a voltmeter directly onto the large starter stud right at the starter. Ground the other probe to the engine block. Jumper the starter relay, and read the meter as the starter is attempting to crank.
Also wiggle those cables around as you jumper the relay
You have seemingly eliminated a lot of possibilities:
Probably not the battery
Probably not an internal engine problem
Probably not starter gear/ ring gear problem
Most likely a defective cable, bad connection, or bad starter.
IT COULD BE a bad starter