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 (Internet Service Provider)?
10. Are you sharing the connection with other computers or p2p sharing programs? If yes, please give details of set up.
11. Do this simple test for us. Using your browser go here: http://www3.limewire.com:6346/ The page should say 'Your test worked!'. What happens when you go there?

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

I've a suspicion your problem is your modem/router so we need to know what model it is. Also, if you have 2 firewalls, disable one of them.