Two things that generally cause clicking noise:
1) Battery, you said you replaced this, make sure the leads are firmly secured, no loose connections. It doesn't make the noise itself, see item 2

2) Starter, the clicking sound is typically the starter as it fails to start the engine. If the starter is fine, it could still fail if it is not getting proper current (and result in clicking noises).
The cheapest way to eliminate the battery is visually inspect everything, confirm there's no erosion or anything on the leads and then jump the battery with a larger battery... I tried jumping my truck with a friends car and it failed, my brother swung by with his truck and it jump started perfectly. New battery or not, maybe something caused it to drain while it was on the shelf. Deep cycle AGM batteries are amazing...
The starter some people say to tap it? I've never had that work, and have always replaced because... Who really wants to be stranded with a truck that won't start? lol.
Good luck.