I suspect there are a few things that you'll need to do.
First and foremost, the Atomic 4 carbs are fairly easy to clean, adjust and rebuild. However, they are also quite prone to getting tiny specks of dirt in the fuel system as well. Remove the carburetor, unscrew the top and carefully remove the float mechanism. Next, using canned air, blow out all the ports and openings where a tiny bit of crud can become lodged. It only takes a sand sized speck of dirt to clog the carburetor.
Now, go to the nearest auto parts store and purchase a can of carburetor cleaner. It's a spray/solvent. Be sure to follow the directions and use this stuff outdoors and position yourself upwind of the cleaning spray--it's nasty stuff. This will clean any residue that may be on the jets, vents, etc...
The most critical step is to set the float level. You'll find instructions on this on the Moyer Marine web site. If the gasket(s) are cracked, you can make new ones from gasket material that's available at any auto parts store.
Next, the flame arrestor must be thoroughly cleaned. It takes a fair amount of work to get the flame arrestor spotless, but unless it is completely free of oil and dirt it has a dramatic effect on whether the engine will start or not. I cannot emphasize this step enough. And, DO NOT try to start the engine without first having the flame arrestor in place--this could be very dangerous.
After reassembling the carburetor and reinstalling it on the engine, lift the fuel pump priming lever a few times to fill the carburetor's fuel bowl. Set the throttle at about 1/4 to 1/3, make sure the transmission is in neutral, pull out the choke all the way and try to start the engine. When the engine begins to start, slowly open the choke and back off on the throttle so the engine does not over-rev. Allow the engine to run at high idle speed until the temperature gauge reaches at least 100 degrees.
There are other things that can cause the engine not to start. The Atomic 4 is an incredible engine, but it needs a few things to keep the internal parts in good working condition. Frequent oil changes are a must--at least for those that do not have an oil filter, which is many of the older models.
Another critical item is the addition of Marvel Mystery Oil, which should be added to the gas tank each time you add gasoline. ::Marvel Mystery Oil::
It is an outstanding product that keeps many, many Atomic 4 engines running smooth as a kitten. It's an excellent top cylinder lubricant that keeps the valves free of corrosion, lubricates the valve seats and protects the valve seals. If those valves are not properly lubed and sealed, the engine will not start.
Hope this helps,