Sounds like your machine came with only one bobbin. If that's so, it may be the wrong bobbin. Also don't forget to insert the needle with the flat side to the left and to thread the needle from right to left. If the machine wasn't advertised as serviced, it may be in deperate need of oiling and greasing. Billy has wonderful tutorials for caring for vintage machines on this board, and is a tremendous source of information.
Maybe if you post a picture of the machine and what came with it, some of the other knowledgable vintage and FW owneres on the board will have some great ideas for you, too.
You might also want to check out the groups on Yahoo dedicated to Vintage Singers and I think there is one also especially for Featherweights.
Good luck! I bought one sight-unseen on the Canadian equivalent of Craigslist. I was very fortunate. So sorry for your bad experience!