There are a couple things that need to be checked. The primary thing is within your voicemail system. There are certain settings that need to be just so for you to receive those messages.
Now, there are 2 different voicemail systems, but in general,here's how it will work.
1) Dial voicemail, enter password
2) Select personal options (should be option 4)
3) Select Message Waiting Indicator On/Off (should be option 1)
The second thing that you need to do, if that doesn't work, is to call VZW tech support and ask them to check the Message Waiting Indicator. That's the little icon you get when you receive a voicemail. If that doesn't fix it, they'll keep on working on it until it's fixed.
I hope this helps!
Alright bear with me here, this is going to take a little experimentation. First, I'm assuming you're using basic voicemail (you have to call the number and listen to prompts).
Second, let me know what options the first menu gives you, and I'll match that against the roadmaps I have or let you know the most likely option.