Yes, leave the back one open, it's an exit for most of the cooling water while operating in water.
I think you should check your fuel lines for an air leak, it's quite common and easy to have a slight leak at the water/fuel/filter separator cup due to the cup is plastic and there's an o-ring at the lip that might fail to seal. This cup screws onto it's base.
Otherwise you can remove the fuel line from the fuel pump and blow with low pressure air backwards toward the fuel tank. before doing this remove the gas cap to avoid pressurizing the fuel tank. You should hear the air bubbling from inside the fuel tank much like a fish tank air pump stone, while forcing air into the fuel line down low through the fuel pickup inside the tank. It should be easy to blow air and no air leaks on the way b/c air leaks will keep the engine from receiving fuel.
If the fuel lines are all air tight and fuel is available to pump from the tank, it's possible your carburetors are internally dirty and must be disassembled and cleaned.