your engine needs 3 things to start and run:gas, ignition spark, and compression. at this point you have verified spark, and you know there is fuel in the float bowl of the carb. so the next step to check would be the compression. this engine has a simple adjustment system, which is called screw and locknut. you will not need to order or change any valve lash shims, but you will need the right procedure to measure the clearance.
but first, lets try a few things:
1:open the intake duct that leads to the carb. as you crank over the engine, spray some aerosol starting fluid, like starting fluid or carb cleaner, and see if the engine starts. if it does, then you know you have a fuel delivery problem. if the engine does not start, then we go to the next step
2:we need to know if there is enough engine compression to ignite the air/fuel mixture in the engine. so you need a compression tester, and a friend to crank the unit over while you hold the gauge. make sure the throttle is held wide open, so you get the best results. if your compression is low, you will need to adjust the valves to see if that is the problem. if the valves are in spec, then there is an engine failure, causing the compression to be too low, wither a bent valve or siezed piston ring. i have seen the push rod fall of the rocker arm in these units a lot, which is a problem they seem to have. so if your compression is low or none, that would be checked along with the valve clearance.