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Since the update, no matter what I try, I get this on the bottom of my screen (Status : Offline). How do I go online ?

In DEFCON installation folder there is defcon.exe and defcon_offline.exe. Your shortcut is probably linked to the first. Make sure you run the latter.

If you are launching it through Galaxy, go More -> Defcon Multiplayer.
Thank you. I found that shortly after I posted and forgot to report it here. Thanks.