Do you have any suggestions?
Yes...my first suggestion is to drain the fuel from the carburetor float bowl and allow the fuel to run for out of the carburetor for a few seconds to allow any of your old fuel in the fuel lines to run out. While the fuel is running out of the carburetor, inspect the inside of the bowl. If you see some discoloration, or any water or foreign material in the bowl, it would be a good idea to clean, or have the carburetor cleaned....IF you need the carburetor cleaned and you'd like to do it yourself then I'd recommend a complete disassembly and soaking of your carburetor in a good carburetor cleaner such as Berryman Chem Dip to get a thorough cleaning. It comes in a 1 gallon pail and you can get it at any auto parts store for around $20.00. Remove, disassemble, and soak for about 30 minutes and spray clean with spray carburetor cleaner. Blow dry with compressed air or allow to air dry if you don't have access to compressed air. Reassemble using a new bowl gasket and needle and seat. The part numbers for those will vary from engine to engine, so if you need those parts, I can refer you to the correct part numbers and an online source to purchase them. Let me know the engine model and spec/type number if you need parts and please let me know if you have any more questions.
We sell used equipment at our dealership, and alot of that equipment is stored over the winter with fuel stabilizer in them. When spring rolls around, we dispose of the stabilized fuel that has been in them and add freshly pumped fuel. The fuel stabilizer keeps your fuel from getting gummy inside the carburetor, but we've found that an engine stored with the fuel stabilized just doesn't like to start on the stabilized fuel thats been in it for several months.
I would try draining the fuel in the carburetor bowl and fuel line first, and if it still won't start and run, I would look into cleaning the carburetor. Try that and let me know how it goes.