I have an '01 vintage Craftsman 6.75 hp self propelled, tried to start it two years ago and the starter rope broke, since I hade newer mowers I set it aside. Wanted to get it running this fall to bag leaves, after replacing the rope I tried to start it. It acted like the engine was trying to backfire, the rope would pull back IN toward the engine at times, it would push vapor out of the exhause but never even fired. Fuel is getting to plug, plug is working well.... It's a Briggs engine.
Did a Google search and found several references to the same model of mower, supposedly if you hit a rock of something the flywheel key will bend or break to save the engine from damage, and with the key damaged the timing will be off far enough the engine will not start and will kick back when pull starting.
What I find odd is, I did hit a rock hard enough a few years back that iot ruined the blade, but when I replaced the blade with a new one, the engine started right up and ran fine then. Wonder why the flywheel key problem would surface two years later?