Make sure the engine thinks it is in neutral when you start it.
There is a neutral safety switch in the front lower casing of the engine, directly below the oil filter. Make sure that...it is plugged in....and it is centered on the detent. It may have come loose or your shift cable may be out of adjustment. The start leads comes to the engine, through this neutral safety switch, and then to your starter solinoid.
Also, depending on how your boat is rigged, you may have another neutral safety switch in the shift box. If it is a Honda shifter and it was installed correctly, there should be none connected. If it is one of the shifters that were made by Morse/Teleflex for Honda, someone may have wired the neutral safety switch in (they should not have).
There are several other things yet to check, but this is the most likely. Just be sure that one of the small leads to your solinoid goes to a good ground. You can probably follow the other wire to the neutral safety switch...through a couple of connectors. Apply 12v anywhere along this lead and you should operate the starter solinoid, thus operating the starter.
Mike