Guys, I (think) finally found the answer.
It seems there is a problem with frontal microphone (yes, iPhone have one). There is one on the right side of frontal earphone (where you put your ear to hear) - if you looking to your phone frontally.
To see if it is, record a frontal video. If no sound was recorded, maybe this is the cause of Siri not work.
Although that, I do not have answer how to fix it (if are problem with cables, software bug, or something else). In my research, I'm believing that is a problem with one of the flats cable. But, at same time, this problem only appeared after iOS 8 update. So, I'm not so sure about my convictions.