It's not easy to determine. 1st you must eliminate all other possibilities such as firewalls, connection devices that use NAT or similar, etc.
I guess one way is to try another one or 2 gnutella clients such as Bearshare or others listed on this forum & see if you have the same problem. There's separate sections on this forum for other Gnutella clients.

Let's see if your port 6346 is open; 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? If you can't reach that page it means the port is blocked. This might be due to the above reasons.

Did you configure your firewall so it allows LW full access (advisable not to have 2 active firewalls b/c they can interfere with each other); Firewall configuration instructions (click on link)

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.