I have a problem with Skyrim from very first play. When I launched Skyrim, and clicked "New Game", first thing which wasn't right was that one of prisoners was just staring at me, saying nothing (As far as I remember, he had script which made him talk to us) Then, when I got to the execution place, nothing happened. I was just sitting in the cart. No player editor, no voices. Can someone please help me? This issue doesn't allow me to play.

Which platform? Did you try doing a clean install of the game and applying the patches?