The serial number may be on the bottom of the machine, under the removable bottom, or under the extension near the bobbin case. It will be stamped on a piece of metal which is attached to the body of the machine. You can look it up here:
http://www.ismacs.net/singer_sewing_...-database.html
qwkslver, that sounds like a problem with the feed dogs. There is a FW Yahoo! group with a lot of knowledgeable people who might be able to tell you how to fix the problem.