Needles often break in more that 2 pieces. Before I mess w/anything else I take off the plate and use a small magnet to see if there are any bits still in the lower part of my machine. Chances are you will be able to see them, but if not, try moving the circular part on the side of the machine that rotates moving the the internal mechanisms slowly and the needle up and down to see if you can tell where (if) it hangs up. the needle won't have to be in position to do this. If there is something hanging it up, the needle shouldn't make a difference. If you can't determine the cause of a "hang up", it's time for a mechanic.
Also, sometimes the needle holder gets moved out of position a bit and the needle isn't directed right into the hole, but hits the side causing it to break. Check to see if any of this is happening. I've found if I know what or where the problem is, I usually don't get stuck with quite as high a bill.
Best of luck with it!