Check to see that Do Not Disturb is not on in your settings.
Settings-Do Not Disturb-Allow calls from everyone, repeated calls set to on (Green Toggle)
Nothing else should show green.
That would have nothing to do with "Do not disturb" that can be a tower issue or a location issue or even the location of your device.
Unfortunately if you don't receive at least 3G ( iPhone displays 1x), your phone won't ring, and goes directly to voicemail. Happens on iPhone 4, 4S & 5. It has happened to several of my clients, myself included (DND can also cause this as you stated).