Alright, Reinstalled ArmA II for the third time and multiplayer looks like it's working.
Added 5 hours 35 minutes later:
I followed the instructions in Placebos' first post on http://forums.bistudio.com/showthread.php?138564
and that solution has FIXED both the "Bad Serial Number given in setup" and the random closing of Combined Operations after opening. Thank you all very much, I appreciate it! ^_^