I'm not a certified small engine mechanic, but all engines need 3 basic things which are AIR, SPARK and FUEL.
Putting these into your situation:
AIR- Should not be a problem. Take off the air filter if you suspect lack of air, but I doubt it.
SPARK- If you're getting spark with the previously described "spark check" or if the engine fires up with the use of "starter fluid", spark is not the problem.
FUEL- Use the Drain to see if there is fuel getting in the "fuel bowl". If you are getting fuel in the "fuel bowl" you're doing good so far. If there's no fuel in the "fuel bowl" clear out or replace the fuel line from the tank to the carburetor. If you have cleaned out the carburetor and ensured fuel is getting through the carburetor to the combustion chamber (cylinder) and it still won't start then I would next suspect the carburetor adjustment settings.
Follow these instructions to get initial settings to get the engine going first and then make final adjustments. I hope all of this helps to get your engine running.