You might have to update your Java....
Uninstall LW and all Java versions on your system. Reboot and then download the JRE offline installer of the newest Java version from here:
http://java.sun.com/j2se/1.5.0/download.jsp
Install it and reboot again, then reinstall LW.

If you have updated from a version older than 4.12 then you might have to find the old preference folder called " .limewire " and delete it as well.

If the above suggestions do not solve the problem, please come back and answer the following questions:
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. Is this a your 1st try at LW or is this a new problem with an experienced user.
12. 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?
13. Try and download a magnet file from here and see what speed you get for it, then post the result as well:http://www.magnetmix.com/video.shtml

__________________

"Never Argue With An Idiot. They Will Drag You Down To Their Level, Then Beat You With Experience"