First, I'd meticulously check every connection on the battery cable wiring. With such a high amperage load in them, a truly tiny amount of resistance greatly reduces the capacity of those cables.
(WARNING: RANT AHEAD)
After they check out as bright and shiney, my $.02 worth is that the engine panel wiring is one of the very few places where Freedom really went fully crappy and cheapo when building my boat, especially the @#%& connector plugs on the engine. My Yanmar 3GMD has all of the engine's wiring coming together to 2 plastic, multi-pin plug connectors at the back of the engine. The mates to those plugs are part of a wiring harness that goes back to the instrument panel. There is actually an "extension cord" in my wiring harness, with another set of plug connectors that are under the aft bunk. There's another set of plug connectors at the instrument panel.
Those connectors aren't worth a damn. They make it fast, easy and idiot-proof for the factory to wire the engine panel, but over time the connectors fail, especially the first set being constantly shaken by the running engine. And, in my case, there are are 4 (!) sets of them. I had the same sort of intermittent "no start" symtoms and the trouble nearly always traced back to those connectors in the wiring harness.
My final, permanant solution was to replace the whole start button circuit with continuous, marine quality wiring, how it should have been done in the first place. I ran a continuous (NO CONNECTORS!), heavy gauge, premire quality, pre-tinned "Anchor" brand wire with adhesive shrink wrapped, pre-tinned copper teminals between the starter solonoid and the key switch / start button. Never a problem since.
And, unrelated, but while I'm at it, the guy at the factory who wired the light in my head compartment using a cheapo automotive butt connector that was just crimped onto the bare, untinned wires, AND THEN HID HIS LAZY, CHEAPO CONNECTION BEHIND A BEAUTIFULLY FITTED AND PERMANANTLY MOUNTED PIECE OF TEAK TRIM, that took me 2 days to find, .... that guy deserves a full-windup kick in the pants.
(Rant over. Whew! Thanks, I feel much better now...)