It looks like there’s two main reasons that Battlefield 3 does not start.
1) You need to update your video card drivers manually – do not use any of the Windows walk-through updates
2) Or, you can remove (TM) from the name of the Battlefield 3 folder
Those are the two most popular fixes for the game, which by the way is certainly a beautiful one. Here is one of my favorite reviews of Battlefield 3 from Gamespot:
When it comes to virtual battlefields, nobody does it quite like the Battlefield series. It has a long history of creating sprawling conflict zones where players have an exhilarating range of ways to make powerful contributions to the war effort. The competitive multiplayer mode in Battlefield 3 stays true to tradition, delivering an online combat experience that is amazingly addictive, immersive, and exciting, with refinements and new elements that make the familiar action feel fresh.