I have to be honest, what you described sound like the battery was slowly dying. That can be caused by the battery or the alternator wasn't charging. The rapid clicking sounds simply like the starter wasn't getting enough power.
Before anything, make sure the battery terminals are clean and tight. Here is a link that you may find helpful
https://www.2carpros.com/articles/everything-goes-dead-when-engine-is-cranked
If the terminals are clean and tight and clean, what I suggest is to first recharge the battery. If you have no charger, most parts stores will do it free of charge. If you take it to a store, have them load test the battery.
If you do it yourself, here are a few links that you may find helpful:
https://www.2carpros.com/articles/how-to-charge-your-car-battery
https://www.2carpros.com/articles/car-battery-load-test
Now, if the battery is good and you recharge it and the car starts, I need you to check the alternator. It is easy to do. All you need is a volt meter or a multi-meter. Here are links you may find helpful:
https://www.2carpros.com/articles/how-to-check-a-car-alternator
https://www.2carpros.com/articles/how-to-use-a-voltmeter
Let me know if you have additional questions and what is found so I can guide you.
Take care,
Joe
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Wednesday, January 22nd, 2020 AT 6:37 PM