I would agree with the suggestions for the most part, so maybe going back to check in detail may help. A few thoughts on how the starter and system work may help asit can be the details that we miss.
When we only get a click when we turn the key, it often works like this. The key closes a circuit to make a solenoid which is just a "switch" that is electrically operated. The click is often that solenoid as it takes very little power to move the contacts and we can often hear them click.
But where things often fail is that the contacts on the solenoid are meant to carry the big power needed to turn the starter and engine. At times those contacts on the solenoid get corroded or burned and that will not pass enough power to turn the starter, so nothing happens except the click!
Or as a second common thing, there is enough battery power getting to the solenoid to move it but not enough to turn the starter.
this is where we need to be sure that what we think is okay , really is doing what it should.
First step is to make sure the start battery is actually still good as even new batteries can be bad or go bad over a few weeks if they are not kept charged. One problem that we often find is that folks get new batteries but store the RV and there are "parasitic drains" which run the battery down. These are things we may not think about and they sneak up on us, if not aware. Things like the radio, any LEDs, etc. draw power even when we think they are turned off.
So what voltage does the battery show? And it certainly can be easy to miss that one end of the cables is not making good contact. One of the more common problems is that the ground cable is loose or corroded where it meets the frame ground or bus bar.
If you look at the resistance from the negative battery post to ground, does it say near zero to indicate good ground?
Also it is easy for the cable from the battery to the solenoid near the starter to be a problem. Have you actually looked or tested that connection?
Another point which I don't know about on your model is if the solenoid is built as part of the starter or a separate item which did not get changed with the starter.
The reason we are both questioning what you have told us is that the system is very little more than we have mentioned, so something is being missed.
1. Turning key makes solenoid click
2. Solenoid contacts close to pass high power and current to starter
3. Starter turns engine
There are lots of details missing on that lineup, but if the solenoid is clicking, a good starter will turn if it is bolted to the engine to have a good ground there and getting good power.
A final thought might be to make sure the engine itself is not frozen up or totally bad, so that it won't move!