This is an iPhone4 not 4S. Brand new 2nd iPhone on my account. When you press voice mail it dials Verizon's voicemail system instead of showing the various voice mail messages. (My other iPhone works fine.) In addition, under Settings-->Phone there is no option to change the voicemail password. I have spent hours upon hours on the phone with Verizon and they cannot resolve this. Anyone see this before?
Have you tried resetting or restoring the iPhone to see if that helps? I know you spent a long time on the phone with VZW but you didn't say what was done to try and resolve the issue. Perhaps try going to your local VZW store (or Apple store if you have one in your area) to see if they can determine what the issue is or if the device needs to be replaced.
Your old voicemail was deleted when you activated your new iPhone 4. Once you have some new voicemail messages, the screen will come up and prompt you for your password and you will be able use the Visual Voicemail as normal. Just call and leave yourself a few messages and this should resolve your issue.