Welcome to Ribnet!
Putting my "high level problem solver" hat on, I would have thought at 8 mins of a "danger" alarm would be enough to kill it proper if it was going to die. The fact the engine still ran means one of three things:
1) false alarm
2) warning alarm (e.g. low oil in tank)
3) your engine was on the brink of self destruction and got away with it by the skin of it's piston rings.
Now, knowing how dodgy electrics can play havoc with control level signals, and also knowing that pretty much all oldschool 2- strokes will happily keep going once fired up with or without battery (the ignition is powered form the engine, rather than the battery), then add it to your lack of PT / starter, my initial guess is also dodgy electrics / battery.
Do you know the history of the boat? A flat battery would do what you described, and if the battery was gubbed, no amount of charging would give you sufficient power to run the PT or the starter, no matter how long it had been charging for.