Hey,

if you've formated your harddrive all your files are gone.
But normally, the key is saved in the registry.

1. Press the "Windows Button" + R
2. Type "regedit" in the window and click ok.
3. Now, the regestryeditor should be open
4. Browse to "HKEY_LOCAL_MACHINE/SOFTWARE/Wow6432Node/Bohemia Interactive Studio/Arma 2 OA
5. There should be a file which is named like "Key" or something. You can open it and edit your key.

If these paths doesen't exists in your registry, then they were deleted by the harddrive formation.

Greets,
pwned