Can you give us a total desciption of your set up:
1. OS version? (eg: win 98)
2. What firewalls you have?
3. ram?
4. HDD space available?
5. Connection type?
6. Modem & router brand name & model numbers?
7. Where are you trying to connect from (home, school, work, etc.)?
These details are vital if you want us to find out what your connection problem is.
8. Which LW & Java versions?

It sounds to me like a combination of modems & routers with internal firewalls. Also your computer may not be properly configured to allow LW: http://www.limewire.com/english/content/firewalls.shtml