This wouldn't be a Sapphire would it? I have one, and had the same trouble.
Check that the thread isn't getting hung up somewhere along the thread path - it can even snag on the spool. If you have the spool on the horizontal spindle, try the vertical. A separate thread holder might help, too.
It's also possible that you nicked the needle plate after you broke a needle. You can use crocus cloth - a very, very fine sandpaper - to smooth out any burrs you might feel.
If this is a Sapphire, make sure it's set up for free motion quilting. There's an item in the tools section for "pivot height," and you can try to set this to -2 --that hint is actually buried in the users manual.
I hope this helps - good luck.
Janet