When you have LW open. Does the icon show that your firewalled(brickwall in front of the globe)?
Do you connect to the internet through a router? Most of them have nat firewalls that need to be configured.
Connection problems? Check here first!
A lot of schools block file sharing software. Ask some of your school mates what port they're using for limewire. Sometimes setting it to a higher port(40000 to 60000) will work.
You could also try deleting the Limewire pref. folder called .limewire, points (2) and (3) in this thread:
Fixes for Limewire when LW isn't operating as it should!. If you delete the pref, folder, make a note of your settings in LW, cause they'll be reset to the default settings.