This happens on this game as well as the Fallout titles. To fix, do the following.
1. Load up the game and select to start a new game.
2. Let the game start and when you're in the opening cinimatic where you're in the cart being taken to Helgen, as soon as you can, bring up the menu and load your stuck save game from inside your new game.
For some reason, this normally fixes it and the game will load from inside your new game. I believe it's a problem with something that sticks in the games cache (not the consoles) that is cleared by starting a new game. Give it a shot and see if that helps you.