Thanks for confirming this and running the PING test.
At this point there is only ONE explanation - Firewall, since everything seems to be working as intended.
Lets take another look at your firewall.
1) Please let me know what Windows version you are using - Xp, Vista or 7?
2) What Anti-Virus/Firewall programs you have installed on your computer?
3) Please do this test - with disabling default Windows Firewall and trying to star the game and Login:
If you are using Windows 7: http://www.youtube.com/watch?v=sl7NdQn3Cjw
If you are using Windows Vista: http://www.youtube.com/watch?v=6GUVLK9oy5g
If you are using Windows XP: http://www.youtube.com/watch?v=5hUXhI3dhow