Sometimes the polymeric end of the needle in the fuel bowl will swell over time and get stuck in the seat. Hence, I keep a carb rebuild kit or a spare needle and seat on hand for this reason. While the polymers are resistant to fuel infusion, over time I believe they develop microscopic scratches which allows some fuel intrusion and thereby results in swelling.
Good Luck!
This is really common. First thing I'd do is wack the carb with something to see if the needle will open then shoot a little compressed air in the fuel inlet to see if that gets it going. More than likely if its happened once it will need to be replaced/rebuilt to keep it from happening again.