Since you provided so much accurate information I have precisely narrowed down the problem to only 1 possible cause and the solution is just 1 click away.
Not really though. Could be any number of things. Check your firewall, it could be blocking Crysis. And I don't just mean your Windows Firewall, I'm talking about the one in your router too.http://www.portforward.com
should be able to help if it's a firewall problem.