I have to pull many, many times, and after a while the engine starts to fire weakly. It will fire weakly 10 or 15 times and die, each time doing a little better. Finally, it fires weakly, doesn't die quite, and slowly picks up speed. Then it takes off and runs. It will restart readily when warm, but if left even 10 minutes, it reverts to the painful starting. The spark is strong (obviously), and I can see gas splash up in the carb throat when I take the air cleaner off and pull the rope. When it does start, it does NOT throw black smoke, as it would if the carb was seriously loaded up with gas, in fact, it throws no smoke at all, and I would bet that in fact it has been starving for gas. Maybe.
I have seen other Briggs engines do this, and I have never figured out what the problem has been. I have done things like take apart the carb and put in a carb kit (mainly, new diaphragm gasket or whatever that thing is called), and sometimes I have "cured" the problem. But if somebody recognizes this syndrome and can tell me what the most likely problem is, I would surely appreciate it.