I would start by cleaning all your battery connections, at the battery and at the motor.
Might be easy to assume this is a new to you boat since you state you don't know if it was winterized, but if it is a new to you boat you need to go through everything and do all the maintenance items before you try and float it.
Mentioning uncertainty about winterization, that needs looking at. Do you live where temperatures get below freezing? If so, then determining what water might be in the block and exhaust is worth the effort. Pull the drain plugs, see what comes out. If you get water that probably means you could have freeze cracks.
Before cranking the motor over the first time, pull the spark plugs. See if you get any water out when you do crank it over.
Can't stress enough, if this boat is an unknown mechanically and maintenance wise, the time to do the maintenance is now, before anything else. Get the Mercruiser Service manual and start in.
