You have this cap and all the parts in the picture? including the silver ground tab?
how do you know that the solenoid is faulty vs. one of the relays or wire harnesses?
I am not all that familiar with inboards.------But what direction does this engine rotate ??----Regular or opposite to automotive ?
One of those timing light tachs would work good for diagnostics.
The air box is just a silencer. Are the carbs opening at exactly the same time? How big is the boat, is the hull clean and what is the rpms when your