@luklas1997 I understand how frustrating this can be as it's happened to me. These two solutions have worked for me in the past when BF3 wouldn't launch via Steam:
Go to C:\ProgramData\Electronic Arts\EA Services\License and delete the file/s there then start the game. The game will create new ones and then it will work. This happens to me every time I have a windows update.
If that doesn't work try this:
Close Origin and all Origin processes in the task manager
Hold the Windows key + R.
In the command box that opens, type %ProgramData%/Origin then click OK.
Delete all the files and folders inside it except for LocalContent
Inside of the LocalContent folder delete the Battlefield 3 folder.
Next open Origin, allow Battlefield 3 to update, then log into Battlelog and join a server and you should be good to go.
