Yup, it was Kindle Support. They're new to the Kindle Touch, just like we are. I got a rep that actually got a Kindle, brought it to his desk, and poked at it until we found the ESN/ICC number.
To get to it, go to the Home screen, enter ;611 in the search box, and press Enter.
As I thought, the Kindle was shipped unactivated. Turns out there wasn't anything wrong with the second one I sent back. Oh well; it's something that they have to deal with because their support agents didn't have that info yet. The one I talked to today said he was entering a ticket for future reference.
Finally, I have a working Kindle Touch 3G!
Side benefit: new, awesome "screensaver" images that don't include dead authors.
