There is one thing I would like you to do. I need to know if you have Norton configured correctly the only way I know of doing this without being there is to un install Norton. What you can do is go to the link below and download Avast anti virus it is free save it to your hard drive then un install Norton then install Avast and turn on Windows firewall. Now with that done follow the instructions below and un install Java and LimeWire.
When you re install if the windows firewall is blocking LimeWire it should pop up and ask if you want to allow it to connect to the Internet click allow if it does. if the problem still exist after this is done then the problem has to be elsewhere like you modem or ISP etc.
Don't get me wrong I think Norton is a good program I just want to see if that is the problem. You can re install it after you run a couple of test.
You will need to install Java and LimeWire manually First go to the first link.You can find Links to java in there Download Java to your hard drive by putting a mark in the save to disc box. Save it to my documents or wherever you save downloads from the internet. Do the same with LimeWire the second link will take you there.
Now with that done click on start then control panel add/remove programs and see if Java is listed on the list if it is uninstall it. Do the same with LimeWire if the un installers were not loaded you may have to manually delete the files. But in most cases this is not necessary.
Now click on the Java installer you saved to your hard drive and follow the instructions after you have completed that do the same with LimeWire.
Please post back and let us know if it worked. If it did not I will give further instructions on manually deleting Java and LimeWire.
http://www.java.com/en/download/manual.jsp Use the offline installer
http://www.limewire.com/english/content/download.shtml