Ok, so i've already tried some of those things (personal firewalls through norton and putting it as an exception etc). I'm not sure how ports and routing work?
Here are the answers to those questions:

1. OS version? Windows 2000 XP
2. What firewalls you have? I've turned off the windows firewall and norton antivirus (permit all for LW)
3. How much ram? I dont know.
4. Hard Disk space available? DOnt kow
5. Connection type? Cable
6. Modem & router brand name & model numbers? Dont know?
7. Where are you trying to connect from (appartment complex,
8. What version of LimeWire - 4.12.11 & Java 1.5.0_10
9. Who is your ISP provider - Atop Communications
10. 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? It works.
11. Are you sharing the connection with other computers or p2p sharing programs? If yes, please give details of set up. No?
12. Is this a your 1st try at LW or is this a new problem with an experienced user. LW old version worked fine, one day it stopped working and i tried to download another version...didnt work.
13. Do you see a brick wall in front of the blue world icon at the bottom of LW's interface? yes.

Update your Java, use the JRE offline installer & remove your old Java version before you install the new one.
http://java.sun.com/javase/downloads/index.jsp

Does your computer connect to a modem or router, or does it just connect straight into the wall for internet? Have a look at any devices that your computer connects to & see if you can find a brand & model.

I can't find anything about that ISP Does the whole complex use them?

There could be a firewall associated with the complex's internet...is there a manager that you could ask?

You could try changing ports, to be honest I don't really know what else to tell you to do at this stage. Within LW tools > options > advanced > firewall config. Change LW's listening port to 64049 > Apply > ok.