I would clean it as well as you can. You don't know that a dinky piece of that broken needle didn't fly down in there. Change to another new needle, coincidences happen and you could have a bent or funky needle in there. When you are cleaning, look very closely at all the places that broken needle might have hit. You could have a ding or a burr from the broken needle bonk that is causing a hangup. As with everything else, make sure that, in your frustration, you didn't put the bobbin in wrong or something simple. Rethread it completely just in case. Hopefully, there is a simple fix. K