Method 1
1. Run Steam as Administrator
2. Go to Library
3. Right click on your Arma II Operation Arrowhead
4. Click on Properties
5. Go to Local Files
6. Press Verify Integrity of Game Cache
7. Launch and see if it works
Method 2
1. Go to Computer
2. Go to Program Files x86
3. Go to Steam
4. Go to Steamapps
5. Go to Common
6. Go to Arma II OA
7. Go to BESetup
8. Click on the file inside and let it update/download
Method 3
1. Go back to your Arma II OA folder
2. Go to BattlEye folder
3. Go to this link (BattlEye website)
http://www.battleye.com/download.html
4. Download BEClient.dll and BEServer.dll for Arma II: Operation Arrowhead Windows 32Bit (If you have 64 bit it does not matter it still works)
5. Go back to the BattlEye folder and replace the BEClient.dll file and BEServer.dll file that is in there or just add them in there if they do not exist.
6. Run Steam as Administrator
7. Run DayZ or Arma II: OA
Note: You can also do this for the regular Arma II as well to see if it works. Just download the Arma II version of BEClient.dll and BEServer.Dll, Method II is also the same. Just go to the Arma II folder in Steamapps/Common to do the same. Do these methods in order if they do not work. For example, do method 2 if method 1 does not work, etc.
If none of these methods work, then sadly you are going to have to reinstall. If reinstalling does not work, you may have had your key stolen or you may just be truly fucked without a solution. I can almost guarantee one of the methods should work.
P.S: I wouldn't mind a thanks if this worked.