First, the female connector has a check valve in it which is why the proper bulb gets hard when not attached. When you attach to the motor the male end opens the check valve, releasing some pressure to the carburetor. If the carburetor float is old, worn or not serviced, you are essentially squeezing fuel directly into the cylinder flooding the motor. An easy way to see this is to remove a spark plug, pressurize the system, crank it over and a bunch of fuel will pour out the cylinder.
Another possible issue is an air leak. Not being able to keep pressure in the fuel system can cause the fuel lines to aspirate (sucking air) not allowing any fuel to the carburetor at all. But you should notice a fuel leak somewhere between the connection at the motor and the carburetor. Pressurize the system and analyze all fuel lines. Look for leaks. When you check your spark plugs, after the above steps, if they are wet and smell of fuel, chances are high you need a carb rebuild kit or a float rebuild at the very least. Extremely easy to do yourself when with minimal skills. My best guess is something, either dirt or fuel corrosion is keeping the float open flooding the motor as this is most common. Also, another possible and likely situation is a bad fuel line anywhere in the system. You can test the line from the tank to primer bulb by pressurizing it unhooked from the motor and inserting a device into the end of the connection to release pressure. Fuel will spray out so be careful. On the motor, if you don't see gray fuel lines, chances are they are collapsed on the inside (which has happened to the tank to engine line on one of my boat) because of using ethonol fuel. If lines anywhere in the fuel system haven't been changed in a few years, I would honestly start there as you should have ethonol rated lines to begin with. After fuel lines are replaced, work from tank to carburetor diagnosing the above suggestions. Fuel systems are easy to work on but without actually seeing what's going on, hard to diagnose. If all the above are in order and still not starting, time to start diagnosing your electrical system. Good luck!
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