It could be several reasons; I try to give you several steps which might help to solve your problem.
At first, please check your latest video-card driver and check what version of the origin client is installed on your computer. Install the newest driver for your video card. Right click in Origin under "my games" on the Battlefield3 icon and choose "Repair".
Login under http://battlelog.battlefield.com/bf3/gate/ and launch the game from the browser without launching it from Origin. If it start right from the battlelog, you should deinstall the Origin client, install the newest client as administrator You find the actual version of origin here: www.origin.com/download. Reinstall Battlefield and try to start it again.
Check the online ports of your connection:
TCP: 80, 443, 9988, 20000-20100, 22990, 17502, 42127
UDP: 3659, 14000-14016, 22990-23006, 25200-25300
For specific instructions on how to open your ports, please visit http://www.portforward.com/ or contact your router manufacturer.
If you have more information about the issue for us, please let us know.
Cheers
Basti
