Why can't I make calls?

I have been facing a really weird problem with my iPhone 5S, which is whenever I make a call or receive one, my iPhone hangs up for about half a minute or so.

The phone actually hangs up the moment I tap on the button(the green button) to pick or make a call.

Due to this I cannot make/receive any call on my iPhone! and my iPhone is now rendered incapable of a mobile phone's primary functionality.

Let me try and explain the situation by writing exact description of the problem:

While making a call, the moment I click that green call button, a translucent black screen appears, and remain for 10-15 seconds....then the usual mute, speaker phone, keypad icons (which appears while making a call) appear. That too, sometimes with few of those round icons appearing as disabled icons.

-- The phone of the person I am calling rings, he picks up and talks, but I hear nothing!!

-- Then I click on the speaker phone button hoping I would hear something on speaker at-least, but I hear nothing.

The very same thing happens when I receive any call.

Except for the normal calls, I am able to make calls via other third party apps like Whatsapp, Skype, etc. But not using the iPhone calling app.

PS. I have reset my iPhone to factory settings twice already, but problem still persist.