Very simple engines can be tested in stages. This is my approach.
1. Spark - Remove the spark plug from the engine. Reattach to the plug wire. Holding the plug by the wire, hold the threads of the plug against the cylinder head and bump the starter. Watch the spark plug to see if you have spark.
- If you do you can move on, if not then the issue lies in your ignition system.
2. Fuel - With the petcock off, remove the fuel line from the inlet of the carb. Place a cup under the end of the line, turn on the petcock and verify that the fuel is flowing.
- If no fuel comes out then you have a problem between the fuel tank and carb inlet.
If you do have fuel, reattach the fuel line to the carb, turn on the petcock, and open the carb bowl drain screw. If you have fuel draining then the issue is not in your fuel delivery to the carb.
- If no fuel drains then the issue is inside the carb (likely the float needle is stuck to the needle seat.