You might be able to ask for a box....say it is for a special occasion or something. Worth a try!
This post must have been fate because:
I received my birthday check from my parents today & the bangle was available online! I'll be sure to post pics when it arrives.
Please post pics of your ring when you get it.
Kitsunegrl, the bracelet is gorgeous! The ring wasn't really doing it for me but the bangle is just TDF! Too bad I can't wear bangles, they slide right off

As for getting a Tiffany ring box, I've found that they do not like to give out the velvet boxes for jewelry that did not originally come with one. I asked for one because I bought a pearl bracelet and wanted to store it in something nicer than the pouch but they refused. Your mother might try taking the ring in for polishing and explaining what happened and asking for a new one. Good luck!