I would suggest calling customer service at 1-800-922-0204 from a landline or another phone and ask them to check your voicemail feature. First to ensure you have it on your line and to assist you to access it from your phone.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
Voicemail is one of the most important features. When you are busy and can't pick up the phone, it's always there for you. No worries, we can help you figure this out. When did this start happening? What other services that are not working besides voicemail? Have you recently forwarded your calls?
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