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One important thing I've found with carbureted engines is don't use the ethanol laced gas that you buy at the local gas station. The ethanol messes up the carburetor in these engines. If the pump at the marina has ethanol, don't use it. It will plug up the little carburetor. Ethanol laced fuel also has a short shelf life compared to straight gasoline. Three months max before separation. I use the ethanol free gas in all my yard equipment, my outboard and my classic cars. My engine problems with this equipment disappeared after changing fuel.
There is really no reason to put ethanol in gasoline. It has to be shipped by truck or rail from the Midwest. It does substitute for some gas but you get less fuel economy and it costs a lot of people cash for repairs. It does, however, make corn farmers deliriously happy and the Senators in those states pleased that they catered to a powerful lobby.
We have ethanol free gas at our marina but the marina only switched to it last year so ask the attendant. We also have two sources in town and we are a small town. Ask around. Your small engines will love you for it.
The first step in checking for your problem would be to check the compression. This will determine if the engine is sound or not. An oil sample sent for analysis is very helpful in reading engine condition. Assuming the engine is sound, the likely culprits are ignition and carburation. Change the points, condenser, rotor, wires and plugs. Look at the plugs. See if the electrodes have damage. excessive oil, etc.
Set the points to the factory setting. If it still doesn't start, pull a plug and sniff it. If it is flooding, the electrode will be sopped in gasoline. A new float will solve the problem. If fuel is not getting to the cylinders, there will be no gas smell. The problem could be as simple as a stuck float or there could be plugged passages caused by ethanol fuel. Then it would require a carb boil out and rebuild. Even if the engine needs a rebuild, the Atomic 4's are a simple engine to rebuild.
Good luck with the troubleshooting.