I would suggest contacting VZW tech support. If it's working on one VZW iPhone but not another one it doesn't appear to be a network issue. I just checked mine to make sure I wasn't experiencing any issues and all is working on my end.
Aburton, I'm sorry you had to endure this issue with your voicemail. I know how important checking and receiving my voicemail is on a daily basis, so I can understand your frustration. I was able to locate reports from our technical team on November 4, 2011
regarding some issues with service within your area. Our wonderful technicians and Engineers have currently resolved those issues. Please let us know if you’re still experiencing problems with your voice mail or any other service issues. Please power cycle all devices on your account to ensure any updates that occurred while fixing the issues were relayed to your phones.