Is it the piece of the needle stuck in there? Check the length against another needle. Is the needle the right size for the machine? Feel up in the hole with a pin and see if you can feel if there is part of the needle screw still in there. You might have to take it to a machine repair shop if the needle screw is broken.
If you had a tiny dermal drill set you might be able to drill out a broken piece but I wouldn't want to try that myself. You run the risk of ruining the threads for the needle screw. Maybe someone else will have some ideas.