Try:
Fixes for Limewire (Delete your LW Prefs folder.)
http://www.limewire.com/english/content/firewalls.shtml
Can you give us a total desciption of your set up:
How much Ram?
HDD space available?
Connection type? (eg: dialup, broadband, cable, etc.)
Modem & router brand name & model numbers?
Where are you trying to connect from (home, school, work, etc.)?
What version of Limewire (LW)
do you have? (Go to LW's menu Help>About LW...)