Ah, looks quite different from ours unfortunately. On the bulky plastic R2 cases, the UPC (or european equivalent which is 13 digits to the US one which is 12) it's on a piece of card that holds the case - and can easily be lost
On the slimline ones (which is just the usual four or so think single cases) it's on the bottom of the box.
I looked all over the box, the case, each individual disc...nothing. I couldn't find it anywhere. Perhaps it was on one of those papers they sometimes include in DVD sets that is just advertisements for other DVDs. I usually just throw that away.
But, in the original Paramount email I got about 2 weeks ago, they said once I supplied the information to them, I should get the replacement disc in 2-4 weeks. So I'll give them another 2 weeks or so. If I don't get anything, I'll have to figure something else out.