Excuse the repeat questions of what you already stated but ...
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?
10. Are you sharing the connection with other computers or p2p sharing programs? If yes, please give details of set up.
11. Is this a your 1st try at LW or is this a new problem with an experienced user.
These details are vital if you want us to find out what your connection problem is.

I'm tending to think your problem is your java. What I'd like t suggest is if you have Java 1.5 to use your Add/Remove Programs control panel to remove java & instead install java 1.4.2 But if you have 1.4.2 then to update to 1.5 but only using the standalone installers. See Fixes for Limewire If that doesn't fix it then unintall LW from the Start menu>Programs>LW>Uninstall & then downld the offline installer of LW from here: http://www.limewire.com/english/content/download.shtml