No video to see....at least not on my version.
Are you sure the battery is strong enough? Have you tried putting jumper cables on battery, and then trying the genset?
When you say that the new solenoid is clicking constantly, do you mean that it clicks even when you don't try to start it? That might indicate a bad start switch.
Also, can you start it from the start switch on the genset itself? (thinking that the remote start switch or wiring is the problem)
If you jump the solenoid, does the starter turn over? (just because the solenoid is new, doesn't mean that it's good:()