For months now, my iPhone 6s voicemail said it was full but wouldn't let me listen to old messages so I could delete them. I know this is not the phone's problem because today I upgraded to the iPhone 7 and am still having the same problem. When I dial 1, it says my voicemail is full and to delete old messages to create room for new messages. I'd like to do just that, but it doesn't play any messages for me to delete. There is also nothing in the voicemail tab when I hit "phone" on my iPhone. Please help! It's frustrating going without voicemail!
We finally figured out how to clear this on my son's phone by doing a reboot. It said it was full when you called in but there were no messages there to actually delete. These are the steps to fix this:
Go into Settings>general>reset>reset network settings.
Your phone will reboot, and when you go into Voicemail everything should be cleared. Call from another phone to verify it lets you leave messages now.