Please excuse the repeats of what you've already supplied but this is a standard set of questions I use:
Can you give us a total description 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?

I must say, "off-hand" it sounds like an isp issue. But let's see 1st.