alternator check
The easiest way I know of to check to see if your alternator is working is to take a voltmeter, and check the battery without the motor running. You should see about 12 Volts. Then start the motor and you should see at least 12.8 volts and usually in the high 13 volt range. If the voltage stays the same or drops, then your alternator, or it's wiring, is not working properly. In my town there is a Starter/alternator rebuilding shop that handles both automotive and Marine alternators. If your town has a decent sized boating community, then I would suspect yours will have one of those shops too.