Actually having a voltage of 12.5v right after being on a charger
can't tell you if it will really accept or hold a charge. Batteries that aren't being discharged but have been on a charger
can hold a "surface charge" which is not indicative of anything. When doing any kind of simple battery testing you need to remove the surface charge by putting a moderate load on the battery for several minutes or a small load for longer. A surface charge won't start an engine more than once, and that would have to be on a bigger battery.
I've found on my own boat that anything over 12v would turn over the motor
enough to start it (a biggish Ford Lehman). It really depends on the size of the battery bank and also to the type of battery and whether the motor
has any issues or not. A bank of 300Ah batteries can start motors with low voltages. A small battery of 80Ah might not be able to. Start batteries can give more juice quickly, as needed to start a motor, but deep cycle batteries give juice slower. A big bank of good deep cycle batteries can usually start any motor, and even a smaller bank if in good shape.
The comments about checking the wiring, etc. are spot on though. If you aren't comfortable doing that you should get someone to help you or hire an electrician and have them show you how things work. One of the very first things I check are connections on the positive AND the negative side of everything to do with motor starting. I have fixed many a boat's starting problem by just tightening the connections of black negative cable going from the batteries or main negative bus - at the engine and at the bus or batteries. Of course you need to do that for the positives as well but those cables
go to more places so they are more complicated.
Places to check are the battery posts, main switch posts, solenoid on the battery, smaller "baby" solenoid that "starts" the bigger solenoid on the starter, connections on the starter/solenoid itself. If the batteries are good and the connections are good you might have an intermittent ignition switch/button problem but for you I would start with the above.
Troubleshooting that and other issues other than corroded cables
and loose connections will usually require a volt/ohm multimeter to check for voltages and excessive resistances in cables, wire, etc. There is also the possibility of an intermittent starter problem. I had one once on my boat where there were a couple of bad spots on the stator and when the starter ended up on those spots it would not work. Other times it started fine.
Hopefully your problems will be on the simple side. You might just need a new battery as someone said above. But always, always check for loose wires. They have a magical way of coming loose on motors and systems with all the rocking and rolling and vibrations on boats/engines.