Lets see if we can get somewhere.
Some have reported that a bad connection at the ignition switch may also cause some of the symptoms.
When the engine turns over is it a fast turn or like the starter is straining to turn the engine?
It could be the starter solenoid.
Once I have ruled out the battery, the next thing I would go for is the starter. But that's just me. The key crank will let me determine this if you follow my drift.
Pull the starter and bench test.

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