If the motor starts but then shuts down, it sounds like perhaps a fuel related issue. I would first check the fuel filter for any debris that may be clogging the screen. This of course, world restrict fuel flow to the carburetor.
My tender's Merc 2-stroke did the same thing on two occasions within the past 8 years. Replacing the inline filter/valve solved the problem.
True Blue . . .
sold the Nauticat