Your CD-key is missing or you use same one as some player on the server. What version of Crysis do you have? (DVD/GoG/Steam/Origin)
PS: If you're advanced user, you can check CD-key in registry:
[code]64-bit Windows: HKLM\\Software\\Wow6432Node\\Electronic Arts\\Electronic Arts\\Crysis\\ergc
32-bit Windows: HKLM\\Software\\Electronic Arts\\Electronic Arts\\Crysis\\ergc[/code]
There's also a tool for changing CD-key on Crysis DVD.
I always make 2 backup from registy, first is location where was Crysis installed and second is CD-key, so even if I install Windows again, I just add this 2 reg files to registry and all working ok ;)