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I would suggest that you have the battery tested first. Autozone will run a free test on it, that will check if the battery can hold charge. With that said, it sounds like your starter is going out. If the battery was weak or had a bad cell in it, waiting for a certain amount of time would not help, it would actually make it worse. A bad battery discharges with time, if the battery was weak and you tried to start the car that would take more charge from the battery and it would not help.
Waiting and trying again, usually indicates the starter is going out. Also the clicking noise is a typical symptom of a bad starter.