Can you give the solonoid a whack if it is stuck?
The click you hear is the solenoid pulling in; lack of sound might be a stuck solenoid, but a click means it is moving.
Simple test: turn on the headlights. Have someone look at them (in daylight) or see how bright they are when dark. Now push the starter button. Do they stay at least 3/4ths as bright? If so, batteries are good and the likely issue is the solenoid or starter. Do the headlights dim out to nothing (or seem to turn off)? If so, batteries are shot or bad wiring from the batteries to the starter, or from chassis ground to battery most negative (you can use a voltmeter to determine which is the problem). This trick works with any car as well (in a car, I use the dome light as I can see it myself, day or night).
Often times very low batteries will give a fast "click-click-click" sound; they have enough juice to pull in the solenoid, but when the starter is connected (at the end of the solenoid travel) the voltage is pulled very low and the solenoid relaxes back; then the batteries pull it in again, and this repeats. Fast clicks at first, gradually slowing, are signs of batteries being dead. If wiring was the problem then the click rate would be constant (I've never experienced this).
I expect that your "new" batteries are shot; there must be some parasitic draw in the truck, or someone forgot to turn off the battery key

(or someone else turned it back on!

). No matter how new they were, spending a week dead in a deep drawdown will ruin them. Take them back for warranty replacement. They might recharge and seem to work but they will not last nearly as long as batteries that have not been drained dead, and they will never be as dependable.
Jim M.
712W and 710M