That happens to everyone when we don't have internet.
could be. GotMtDeW can you try to put Digital Paintball 2 on the "expection list"? Some thing similar happened with me, but it was for League of Legends, and I had to put LoL on the execption list. By the looks of your screen shot, I'm going to assume your on Windows 7. Go to the controll panel->find Windows firewall->go into its option->find a "execption list"(I believe it might have a different name to it but read the description)->add/check off Digital paintball 2. Before you do this though, turn of Windows Firewall(and anyother firewalls too) then try running it. If paintball does connect then do the above.
Can you put up a screen shot of your console when your trying to log in and press “~“ and while your trying to connect can you start up Task Manger and choose "network" it will show a network graph.
Also, assuming it might not work, can you also tell us if you can play the game(meaning can you still play without logging in? Online, not offline)