For anybody to be able to help you, you will need to give us a bit more information.
What version of LimeWire are you running?
On what Operating system does your computer run? Vista or Windows XP? etc....
Do you have a Firewall?
And if you do.. is it set to allow limewire access to the Internet?
Is LimeWire acting normally in every other way?
What symbols are indicating near the globe at the bottom left hand corner of LimeWire?