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You said you have battery voltage at the starter. The only other thing you can check is to make sure you have voltage at the exciter wire (the small wire that triggers the solenoid)
If battery voltage is good, and you have power at the exciter wire, then it's a bad starter, plain and simple
If you tried to manually jump power to the small solenoid wire from the big battery cable and still nothing happened, you can pretty much rule it a bad starter and not something else in the sequence ahead of the starter
Depending on the mileage, it's probably about due to be replaced. But make sure you check to ensure that both the big battery wire has power, and the small exciter wire shows power when someone turns the key to try and start it. If they do, replace the starter. If not, let me know and I'll help you troubleshoot it further
You have to remember that it is nothing more than a large electric motor. If there is a bad spot in the motor, it may do nothing, but if it turns a bit so it is not on the bad spot anymore, then it'll spin right over