Cannot set up voicemail message

When I get the option for choosing which type of message to play, press 1 for one kind, 2 for another, and press 3 for a custom message, it never accepts any key press. Not 1, 2, or 3. Not from any phone. Not if I press it multiple times or hold it for a few seconds. "Sorry you're having trouble; good bye." As a result, I have no voice mail. 

What gives?