I've had the same issue with my Westerbeke and both times it was the fuel shutoff solenoid. They apparently crap out frequently because once I figured out what is was, I recognized that part in the used part bin of my boat. Very simple to change out.
It looks like this. Not sure of your specific model, but look around and you can find deals on them. Check Ebay for overstocks.
Westerbeke, Solenoid, Fuel 12Vdc, 023041