Just another update - in case anyone else is reading this thread.
I got an email from Singer today. They are willing to pay to ship my old machine back and exchange it for a Singer 2662 CL: http://www.amazon.com/exec/obidos/ASIN/B000C9MVFG/ref=nosim/coffeeresearch109506-20
I paid $400 for my Singer, but I figured I'm glad to be getting a working replacement, and since the machine is a few years old, this is actually a very comparable machine! Hopefully it will work!
So all in all, Singer's customer service was very good, and the replacement was generous - they are definitely standing behind their product, and I was pleased to see that.