Lots of good ideas here but so scattered as to be difficult to use. First of all, don't start replacing things until you confirm that it is a problem. You'll have new widgets but will be very lucky to actually solve the issue. Second, this kind of thing can be VERY difficult to trace down and fix. You should start with the most likely suspects and if that doesn't sort it out, then go step by step through the whole system.
I am a very experienced marine electrical
tech and have troubleshot and fixed hundreds of start "system" issues. Anything and everything can break so any statements to the contrary are just flat wrong.
The numero uno cause of starter problems are wiring
connections, especially at the engine, but everywhere too. Check the big wires to the starter (positive and negative) including the negative to the engine block. Check the terminals/crimps themselves. Voltage checks will not tell you how good they are as a really poor connection/path will register good voltage. No voltage means no connectivity at all. Check connections at the battery
too, and at the battery
switch(es). Loose connections can cause intermittent problems. I've fixed more loose connections/bad terminals than any other issue. Yet this is the easiest thing for the amateur to check. The terminals have to be crimped well and sometimes this is not obvious by just looking. Wiggle. I have had 2/0 wire pull out of starter terminals that were not properly crimped. Check the wiring
at the battery too, and at the battery switch.
Then check the solenoid as mentioned several times above. If it clicks then it MAY be OK but at least it is trying. If no clicks you can try jumping around the solenoid to see if the starter works but you best know what you are doing or you can screw the whole works up. I am hoping this is a diesel
and not gas because you will make sparks.
If the starter is getting a good juice and the solenoid is working, then it might actually be the starter itself which could have a couple of bad spots on the commutator OR the brushes
may be bad. We had a starter that would work some of the time and not others. I went through the entire system and isolated the problem to the starter. Took it to the local dirt-floor mechanic
(in Vanuatu) and the said the starter was fine and told me (basically that I was stupid). I took it back and it still didn't work. Well - it just depended on whether the starter rotor ended up after the last start whether it would start or not. You can try whacking it with a mallet to see if that causes it to start. But it could be a sticking or weak solenoid or the same problem I had. Take the starter to a good mechanic
You might have a "baby" solenoid that is between the key switch and the starter solenoid as well. Solenoids fail all the time. Keep spares if you have this set up. Solenoids don't need as much juice as the starter but they do have to have enough current
to operate - not just voltage.
The wiring between the key switch and the start button to the engine needs to be checked too. You can use your Ohms meter to check a lot of this wiring after verifying you have voltage. Voltage is easier to check first. ALWAYS check the ground connections. You need good ground (DC negative) to everything - panel to engine to battery. You can test Ohms on the key switch as well. They routinely go bad. Same for the start button.
Of course, your start battery has to be good as well.
The engine alarm
you should hear when you turn on the key switch turns off from an oil
pressure switch (normally on). When the engine starts and builds oil
pressure it should go off. If no alarm
then you have a bad connection or bad oil pressure switch or bad key switch or bad alarm buzzer. The key switch powers the buzzer so long as the oil pressure switch remains on. The buzzer may be used for other things as well but that is the sorta/kinda starter related function.
Good luck. Again - go for the most likely issues first - loose connections, terminals, solenoids, switches. Then go through section by section to track down any other problems but I bet you get it fixed before that - BUT it may get down to that.
Please don't take me apart if I left out something. I did this off the top of my head
and just trying to be helpful. It should point you in the right direction.