So the ring was NOT insured yet, right? I would take an active role and start looking in Pawn Shops and Ebay as soon as possible. I've had bad experiences with lost items and the police. In the past, if always just seemed like they couldn't give a $hit, but maybe that's just the rudeness of the NYPD. I'm so sorry this happend to you! Just try to stay positive, and who knows, it might just turn up!