straight to voicemail

I have an iPhone 4, and it is sending ALL of my incoming calls straight to voicemail. I have good service, and it doesn't matter where I am. The ringer is on. It is not in Airplane Mode.

Everything else - apps, texting, voicemail, outgoing calls, surfing the web - works just fine.

I backed up my phone and restored factory settings. It still doesn't work. I reset the network settings. It still doesn't work. I've done a hard reboot several times. It still doesn't work. I popped out the SIM card and replaced it. It still doesn't work. I deleted tons of old voicemails. It still doesn't work.

Any ideas?