Hard Start / Won’t start

Please help. Parked my 19.5 hp Briggs mower and could not start a week later. Turns over and pops from the carb. Every once in a while it will start and run pretty good. Then after shut down, won’t restart. Strong spark, new plug, replaced carb, new fuel filter, fuel pump pumps plenty of fuel. Fresh fuel. Fuel solenoid working as it should. Compression is 120 ish. Valve lash checked and within spec. Removed head and lapped the valves. New head gasket. The flywheel woodruff key has not sheared or slipped at all. The only thing I have not replaced or reworked is the coil, but my spark is good. I’m stumped. What could the issue be. It does pop from the carb. That’s not right. Any help would be most appreciated because I’ll have to get a new mower if I can’t fix it. Thanks.

Tried this many times. No response at all, except for more popping from the carb. Even directly into the cyl, and nothing.

Well, seems you have compression, you have spark, you have fuel.
 
The engine should run IF all things are timed correctly. 
 
I would pull the main shroud and valve cover.   Examine and slowly
turn the engine over (by hand).  Pay close attention to the time the valves open and close
(compression stroke), where the flywheel magnet is AND especially WHERE the piston is.
 
Of course the piston must be very close to TDC, the valves closed and flywheel spark magnets
in line with the coil for the engine to run.   I suspect one of those is not in sync.. 
 
I'd be leaning towards the cam possibly being an issue...
 
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