This is actually very common. Most of the time all it is is castor oil build up that hardened and locked it up. You can pre lube the engine with a few drops of after run oil or some fuel (automatic transmision fluid or air tool oil works well too) then I like to use my monocoat heat gun and heat up the engine and allow to cool just enough that I can touch it again. Repeat this a few times... This will "melt" for lack of a better word your coagulated oil residue. If you do not have a monocoat heat gun you can send the wife shopping for an hour or so and use her oven.

this should free everything up but you may still have now free moving chunks of old castor oil in the engine. The place where this would cause the most problems is in the needle valve assembly. Remove the needle and clean it with a mild solvent and rinse with fuel. Observe your O-rings if so equiped. Then I like to use carburetor cleaner and blow out the needle valve housing... Do this with the carb removed from the engine and mind the carburetor O-ring as carb cleaner will deteriorate the rubber over a period of time.