Can you give us a total desciption of your set up:
1. OS version? (eg: Windows 98)
2. What firewalls you have?
3. 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.

Do this simple test for us. Using your browser go here: http://www.grc.com/port_6346.htm (Press Probe this port button) Does it say open or closed?

If you do not get open or closed results then try this one: http://home.no.net/tgrumpy/ct/dex.php

Configure your firewall (only need one firewall to be active: 2 can interfere with each other!); instructions to allow LW full access: http://www.limewire.com/english/content/firewalls.shtml