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.

May I recommend you either or both update your java & try deleting your LW Preferences folder whilst LW is closed; instructions here: Fixes for Limewire (Java link in that link.) If you have java 1.4.2 then update to java 1.5. But sometimes 1.5 doesn't work well on some people's systems so you should unintall java using the add/remove prog control panel & then install the other java. (But install it from your comp, not over the net; save the installer to your comp & then install it from your comp, not over the net!!!)