I don't really know anything about Dixie Narco machines - I don't think they are generally considered very collectible as most were push-button machines, but it should have a stamped ID tag on it somewhere like pretty much all machines do.
If not, your best bet is to either:
1) Scroll through them here and try to match up what you've got:
http://soda-machines.com/index.php?option=com_content&task=category§ionid=3&id=45&Itemid=14-or-
2) You may be able to send the company a picture of what you have for ID purposes. Dixie Narco is still around and making machines, not sure if their customer service would be helpful or not.
Good luck!
Jim