This is what I would do.
1. Remove the bobbin (and bobbin case, if you have one).
2. Remove the metal plate that is under the foot. (On some machines, they pop out. On others, you have to use a screwdriver.)
3. Once you have both of those out, take a flashlight and look at the machinery the best you can. Brush out all the dust and lint - you can use a pipe cleaner to get in the narrow places. Use tweezers to remove any stuck pieces of thread. If you can see the needle bit, use tweezers to try to remove it.
4. If you can't see any obvious broken pieces, try oiling the race (the part that moves under the needle).
5. Remove the upper thread.
6. Re-thread the bobbin, replace the plate, then thread the upper thread (with the foot & needle UP).
If you still can't get it to work, it's probably time to call in the professionals.