your prob description indicates engine is not getting sufficient fuel rather than ignition prob. Remove/clean the fuel lines, fuel filter, fuel tank. Then ck to see that you are getting good fuel flow to carb. If so and engine still doesn't start easily, remove/clean the carb.
If still no luck, this may be one of the briggs engines that are touchy about valve adjustment... mebbe another poster familiar with such can comment on that.

Symptoms are not typical of needing valves adjusted. These engines will run on one cylinder. Will it start, run if you dribble a little gasoline directly into the carb? Have you checked the spark to see that you have good fire?

Walt Conner

Commonly, these seem to accumulate water in the carb bowl and get to that magic point that nothing happens. You can remove the bowl with the carb on the machine if you are somewhat skillful. A stubby straight screwdriver works. You will also need to check if the solenoid below the carb is working- should hear/ feel a click w/ the ignition turned from off to on. You will need to remove the governor bracket bolts and watch the springs if you go this route for bowl access. Be cautious of the o-ring that fits over the pipe assy on the inside. As stated above, flush the line, replace the fuel filter if water/ debris is found.