Sorry to hear about your problem, to answer your questions the engines do not need to be running to Heat or cool your boat. It is imperative that the unit be pumping water to cool the AC/Heat unit.
You didn't mention if there is a strainer after the seacock to collect any debris from the lake, that must be periodically cleaned if you don't it could become clogged.
I would try the unit in AC mode for a period of time if it is cooling properly the unit should cycle on and off once the desired temperture is achieved. The same holds true for the heat cycle. The cooling water is required for both cycles. Also this water line must be winterized every fall to prevent freezing.
The Marine unit is very similar to house AC/Heat pump except it is cooled by water in stead of air.
You didn't mention if there is a strainer after the seacock to collect any debris from the lake, that must be periodically cleaned if you don't it could become clogged.
I would try the unit in AC mode for a period of time if it is cooling properly the unit should cycle on and off once the desired temperture is achieved. The same holds true for the heat cycle. The cooling water is required for both cycles. Also this water line must be winterized every fall to prevent freezing.
The Marine unit is very similar to house AC/Heat pump except it is cooled by water in stead of air.