The next (and final) chapter in this voicemail saga you're not going to believe. After first dealing with ATT support who lost all my passwords - including the password for my wi-fi router - and then dealing with U-Verse support trying to recover the password to my router, the U-Verse support guy finally gave up and said all he could do was to send me another router (no charge) and I could send the old one back to him. So then I wait a few days for the package. All the while, I'm burning up my data allowance and approaching the end of it without being billed for excess usage.
Finally, the package arrived and he sent - A BLEEPING MODEM!! Can you believe this nonsense?? There's nothing wrong with my modem! I think the lunatics are running the asylum!!
Meanwhile, I spent most of the next night awake trying various things and the next morning I decided to contact Cisco who made my router. Long story short - the Cisco support folks helped me recover my password so I didn't need a new router - all I needed was the password. And they did this at NO CHARGE even though my router was long out of warranty. KUDOS to the folks at Cisco.
And now, all's well that ends well. I hope the things I've learned through this fiasco might help some of you other iPhone users in the future....