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. Is this a your 1st try at LW or is this a new problem with an experienced user.
11. Were you able to use LW before this started happening? At which point in time did it start happening?

* Try deleting your LW Preferences folder whilst LW is closed; instructions here: Fixes for Limewire
If that doesn't fix it then uninstall your Java & re-install it from the link I gave you. Don't install over the net but save it to your computer 1st.