No it isn't run from a solenoid, its run by the cdi direct. Yes that could be pricy but your not there yet. Don't automatically lube cables as some are designed with liners sensitive to hydrocarbon based lube which can swell. Use a silicone based lube if you must.
Unplugging the power valve should make no difference to the bike actually running, massive difference to power and rideability but it will happily start and run.
Are you getting a spark? Or have you tested it on something else?
I'm still thinking electrica not the cdi (yet) either. You have done things like checking the ignition switch is switching all its supposed to, wouldn't be the first time that's been at fault, or the kill switch, all go through the headlight the garage got wrong......