If it has a fully charged battery even if the alternator were bad it would still start. Are you positive you cleaned the battery cables very clean and tightened them properly. Clicking is usually a battery or starter issue never just replace parts without having them tested on the vehicle or bench tested.

Follow the negative battery cable from the battery and make sure it is securely grounded at the engine and frame, and grab both battery clamps and make sure they are tight on the battery terminals. Also get a voltmeter and check the actual voltage, also useful for voltage drop testing when you have one.

Alternator is not working. Please do mention transmission type and other relevant info while posting a question, that will help u get the most correct answer. :) if it is manual tranny, do a bump start & if it works then surely it's alternator.

Have you possibly tried the alternator? That could be going or gone bad.

When I go to start my car (97' Toyota Corolla) there is a single click then nothing. I just bought the battery and a battery charger says it's fine, I just put a different starter in, same noise. Most of the time if the car had ran for a bit, it would fire up on the first try. But now I can't get it to start at all. ANY ideas?