Problem solved! It's an account issue. With the flood of new accounts, the Apple and AT&T servers were overwhelmed, and while playing catch-up, some wireless accounts were set up incorrectly, with multiple features not activated.
Call AT&T customer service and follow the phone tree to wireless account issues (not to tech problems with iPhone -- that will get you transferred to Apple). The guy on the phone was familiar with the problem, was able to correct my account in five minutes, and was extremely friendly.