So this is a generator that you just installed, replacing a different generator. Is that right? In other words, this has never run, and the installation may or may not be correct, including all the wiring.
I ask just so we know where we are starting from, namely ground zero.
And you said that the stop switch activated the solenoid? From what people who are familiar with this unit have told you, that's exactly the opposite of what is supposed to happen.
I don't mean any offense, but you seem to be really over your head with this, and somewhat randomly doing things. You are probably a lot better off getting someone on board who knows what they are doing, and making sure they know that they need to check the installation starting from step one. At a minimum, it sounds like your energize-to-run solenoid is wired as an energize-to-stop. With that, it will never start - kind of like you are experiencing.