There are several things that can cause that, all difficult to hunt down. There are several relays and a transmission control module (computer) that need to send/receive power and send signals to the tranny and the shifter. A loose or corroded connection on any of them could cause the problem.
What solenoid clicks? Are you talking about turning the ignition key or something else? The engine won't start unless it can verify the shifter is in neutral, so a dead shifter probably prevents normal engine start.
Former owner of 2004 American Tradition and several other RVs
Home is in the Ocala Nat'l Forest near Ocala, FL
Summers in Black Mountain, NC