Sounds like you need to configure your firewalls for a start: http://www.limewire.com/english/content/firewalls.shtml
Also make sure your Java is up to date, see: Fixes for Limewire


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.
These details are vital if you want us to find out what your connection problem is.

I forgot to ask 9. Who is your ISP provider? If you use a proxy have you set LW up to cater for it.