I'm not really asking for help with my voicemail, since I found an external solution, but the problem is a bit strange. After someone leaves a voicemail, I call in to get my messages. When the prompt asks for my pin number, the screen goes blank. I can wait a few seconds and it comes back. Then I tap the icon that says "keypad" and I can type 2 digits of my pin, then the screen goes blank when trying to hit the third digit. It doesn't matter how long I wait to tap the third digit, the screen always goes blank. It's almost as if someone is watching over my shoulder and laughing at me trying to get my pin entered without the screen going blank.
The solution I found was in a voicemail app. It is called YouMail and it has several nice features - and the screen doesn't go blank when trying to type in my voicemail pin.