Small Engines (Lawn Mowers, etc.): Ruff running engine

Question
I have a small Honda generator (EG 650) with a Honda G100 engine. My problem is I now have it running but will only run with the choke close and it runs ruff, going from slow almost dying to running fast. But will die if I open the choke. Have replaced the spark plug, cleaned the air filter, taken the carb apart and cleaned it. There is a dent it the fuel tank but have got it almost out so the fuel cap fits better. Any ideas would be great.

Answer
It is running lean.  Will it run if the gas cap is loose?

Did you blow compressed air, from an air compressor, through all of the carburetor orifices?

Did you spray carburetor cleaner through all of the carburetor orifices to make sure none of them are clogged?

Eric