It would help if you can figure out the model of the machine. Try Googling "vintage Singer sewing machine" and then click on "images" to see if you can match one of the images to the machine. Some models are worth more than other models. I take it this is not a treadle machine? "Very old" means different things to different people.
There are vintage Singer groups on groups.yahoo.com that you might want to join if you decide to fix up the machine. There are ways of removing rust and unfreezing an old machine, but you need to know how to do it.