As Ed/Rinker has said, solenoids come with the starter, however that doesn't mean it's ok!
Buy a good multimeter, Draper are the best.....
and check the voltage across the terminals to the solenoid, should be about 12.7V ish. This will give you a clue to whether you are getting full energy to the starter at first turn.
Several things affect starters on boats, damp, battery, wire corrosion and the throttle lever in gear. Unlikely it's the battery if it turns over freely, if it was the throttle lever it would not let power go to the solenoid.
I think the solenoid terminals are either very slightly corroded or there is not enough current on the first turn to throw the solenoid spindle to actuate the high tension to the starter. This points to your obsevation that the earth is poor or the spindle is sticking inside the solenoid.
Land Rover....making mechanics out of owners for 50 yrs.
Cheap fresh oil is better than expensive dirty oil...