The keyway for the flywheel on most all Briggs engines is fitted with a soft key that will shear in the event of sudden impact, such as the blade hitting a big rock or something. The key shears which changes the timing enough to kill the engine on the next power stroke to prevent further damage.
If there have been some slight impacts over time, the key can shear just enough to throw the timing off and make it very difficult to start. These keys can be purchased almost anywhere that Briggs parts are sold.
While you're checking the flywheel, knock any rust off of it with some sandpaper or some such. Theoretically this rust should have nothing to do with preventing spark, but in real life it seems to make a difference.
Another thing is if you run completely out of gas, then fill it up, you sometimes have to blow into the vent hole on the gas cap to push enough fuel into the feed well for it to start.
Lastly, I am assuming that this is a new enough model that it does not have points. If it has points, adjust them and see that they are perfectly clean and no oily film on the contacts.
Hope this helps, if you still have trouble, email me and we'll go through some more things. My daughter and I race souped up Briggs powered Go Karts, so I'm somewhat familiar with the breed.