Very happy you found your likely problem. A macerator pump will not pump waste through a closed valve!
But to follow up...
Depending on where you are boating in Florida, waste discharge rules could be more stringent than Federal rules. Absent a manual lockout device, a removable key switch for example, I suggest you keep the pump-out seacock closed when operating in State waters. An additional benefit, operating the seacock frequently will prevent the valve from seizing-up and rounding the stem/handle in the future. I suspect the seized-up seacock was the initial root cause that resulted in the tank being replaced (unless it froze and busted).
From your photograph, your waste-holding tank discharge pump looks to be a Jabsco Series 18590, or similar, macerator pump. This macerator pump is of an impeller-type, similar to the cooling water pump on an outboard motor. This type of pump doesn't have/require the "duckbill" valve most of us are expecting from our experience with diaphragm-displacement type waste pumps. So don't worry about a reversed duckbill valve (your pump no, displacement pump yes, very possible to reverse).
When the seacock is repaired/replaced and open, you could still have blockages and plugging in a) the intake tube from the pump inlet and dropping down into the holding tank (and yes, it is OK that some air can escape at the grommets where inlet and outlet tubes enter the holding tank, you just don't want waste sloshing out here), b) the pump impeller and volute, c) the pump macerator cutter/chopper, or d) the outlet hoses leading from the pump to the seacock.
It is possible that the pump impeller and associated parts might be worn/damaged as well. If you have repaired and opened the seacock, eliminated all possible blockages/plugging, and the pump still doesn't pump (but the motor runs), you can get and install a pump rebuild kit. My guess is that a rebuild kit may cost as much as a new pump, and replacing the pump will likely be much easier than installing the rebuild kit.