My guess is it's a firewall issue or router device issue. It's only recommended to use one firewall as using 2 can interfere with each other. Instructions on configuring them for LW can be found here:
http://www.limewire.com/english/content/firewalls.shtml
If that doesn't work then try deleting your LW Preferences folder whilst LW is closed; instructions here:
Fixes for Limewire Consider re-installing Java also.
If that doesn't work then:
Can you give us a total desciption of your set up:
1. OS version? (eg: Windows 98)
2. What firewalls you have?
3. How much ram?
4. Hard Disk space available?
5. Connection type? (eg: dialup, broadband, cable, etc.)
6. Modem & router brand name & model numbers?
7. Where are you trying to connect from (home, school, work, etc.)?
8. What version of Limewire (LW) & Java do you have? (Go to LW's menu Help>About LW...) Will show both LW & Java version.
9. Who is your isp provider?
10. Is this a your 1st try at LW or is this a new problem with an experienced user.