It's important that you just set it up exactly as I described for now, for troubleshooting purposes. You can change it later, after we figure out what's wrong.
Also, while you are on the advanced settings page, do this, even though it seems pointless: On "Forwarding options", change the setting to "Ring my other phones before going to voicemail". Click the "Save" button. Go back to that same setting again, and change it to "Go straight to voicemail". Click "Save" again.
You said you are using *71 to configure conditional call forwarding. Please confirm that you have a Verizon Wireless mobile phone account, and not an account with a MVNO (reseller) like Page Plus or Straight Talk. Also, what model phone is it?