I have a similar problem, but not exactly the same. My Galaxy S4 (on Verizon) "sometimes" does not ring, and other times does. Seems like first call in the morning from certain individuals the phone does not ring (ring tone is on, full blast, no blocking). I get the voicemail message, and when I check my incoming call log, and no call is recorded as incoming. When I check the time of the incoming voicemail and compare it to the call log, it does not show a corresponding incoming call at that time. When I call the person and ask them to call again, the next incoming call from them works fine, rings nice and loud. I just got the phone a couple weeks ago, and returned it for this problem. Tech said it was bad hardware and replaced it. New one is doing the same thing. HELP???