iPhone Phone app doesn't launch

[naughty90s]

I came across the weirdest glitch I have ever met on my iPhone. When I launch my phone app (or what is it called like? the native one to make calls), it just doesn't start getting stuck loading. Sometimes it does show my recently dialled numbers, but the screen stays inactive. I can make calls from iMessage app though: I do manage to dial a number from my repliers info.
Tried a soft-reset, hard-reset with my iCloud backup restore - didn't help. Any tips?

 

[naughty90s]

Looks like the screenshot didn't attach properly. Here's a link to it.

 

[naughty90s]

Also noticed that I can't access Phone section in Settings. The device is 5S running iOS 9.1, not jailbroken.