This is a continuation of a similar thread that I guess is closed. I had this issue as well. I ordered the complete carburetor with gaskets from Briggs and Stratton website. It was $25 plus another $10 for tax and s/h. Very simple to replace. Drop the gas tank and it comes with it. Primed 3 times and it fired right up.
I spent days cleaning the carb and trying to get it to run without progress, sometimes it would run for a few seconds. I think it is the rubber membrane between the carb and the gas tank stretches out and doesn't work properly anymore. But I ordered the whole thing just in case there was more to it. Lawn mower shop estimated $75, $35 minimum to diagnose if chose to decline the repair.

Hi,
There check valves in the primer circuit that can stick. Usually you will feel resistance in the circuits as the backside of the primer fills on the third or fourth push. I have never dependably been assured of a prime without removine the air cleaner and looking down into throat to see a stream of fuel.
Peace,
Clarke