I had the same situation with my CB400F. I would hit the starter button, lights would dim, but nothing on the solenoid, no click. So i pulled the cap off the solenoid, careful not to pull the wires out, just the cap, cleaned the contact points, reinstalled. Nothing same thing. but this time I tracked down all the wiring, and lead me to the actual starter button. pulled the handle bar assembly apart (not completely just enough to get cleaner in there), sprayed some electic cleaner in there, (almost like carb cleaner but for electronics) and then everything worked! So the button wasn't making a good enough contact to the ground inside the handle bar switch.
I would suggest checking the starter button.