Is your apartment part of any school accommodation? Some apartment complexes have a separate firewall & may also block certain things...if the test page isn't working then something's blocking LW's default port. Lots of school accommodation does block p2p. Do you know if anyone else in the apartments can use LW, or any p2p?

To check if your XP firewall is turned off, go start > control panel > double click on Windows Firewall...it will show if it's on or off.

You could try connecting using a different port. In LW tools > options > advanced > firewall config, from there you can change LW's listening port. Try port 64049.