I see that a lot of people here got a problems with the server connection. (Authentication Fail (3) error)
The most common reason for this is the serial key problem.
I got the same problem, because I've lost my Crysis user's manual with the CDKEY (It was a long time...

)
Anyway, there is a possibility to play for the people who got this problem.
How to play:-First of all you have to download Hamachi (required to create Virtual Private Network) here: https://secure.logmein.com/hamachi.msi
-Then you have to install it. It's really simple.
-Run Hamachi, click on "Network">"Connect to existing network..."
-And type following:
identificator: mechwarriorlivinglegends
password: mechwarriorlivinglegendsThat's it. Since now you got LAN connection via internet with all the people who also in this network, so we can play using LAN not Internet.
Somebody have to create LAN game and others have to go "Local Network Game>>Connect to IP" and type the Hamachi IP address(not external) of the person who created the game.
Update: If you get "Kicked from server" when trying to connect to the Hamachi server, try to go "Multiplayer>>Internet Game>>Connect to IP" and type Hamachi server IP there (not in the LAN section).