The bobbin case isn't supposed to move around, only the hook underneath it is. If you've broken a needle, and the thread isn't picking up, you've knocked the timing off. Usually on those machines, the needle bar needs to be put back in place. Your local shop is likely to charge you around $85 to do that simple thing. I'd put that money into a better machine that will hold a timing setting.
And throw away the big "quilting" pins, and get some fine or extra fine "patchwork" pins. They don't knock the timing out when you run over them.