Perhaps a sheared timing key, like was mentioned, above is causing your problems. If there was a backfire, I think the flywheel key is designed to shear off to prevent further damage.
If you verified that there is fuel getting to the carb, and that there is spark, and a little compression, … then all you need is to make sure the spark happens at the right time, which is the flywheel timing key.
You need to remove the pull start/recoil and fan shroud to reveal the glory that is the flywheel.
Suck, squeeze, bang, then blow…
In that order.