Can you give us a total desciption of your set up:
1. OS version? 10.2.?
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) do you have? (Go to LW's menu Help>About LW...) Will show both LW & Java version.

Wireless routers tend to have internal firewalls. This might be your problem. But we need to know what type it is (eg: apple Airport)