What versions of LW & Java are you using (in LW click help > about LimeWire & you'll see the versions you're using)? Did you try changing Java versions as I suggested before? Did you also delete your preferences folder?

Your LW must be pretty old if there's no firewall icon. Some people can successfully run really old versions, others run into problems. If you have the installer for your old version (sounds like you do, if you've reinstalled a few times), you could try the latest LW 4.12.11. Just download the free basic version & see if it connects. Installing a new version will automatically remove the old one, so if you didn't have the Pro installer saved...you'd lose that version completely
Lime Wire » Download LimeWire

In LW go tools > options > bug reports > view example. Scroll down to 'recieved incoming this session'...if it's false, there's probably a firewall problem somewhere. In that case, double check that your XP firewall's off & that your ZA's configured to allow LW. You could also try port forwarding for your router. The instructions are here.
PortForward.com - Free Help Setting up Your Router or Firewall

Don't forget the step of setting up a static IP address. LW's listening port, port in the 'manual port forward' box & port forwarded within a router must all be the same number.

A few people have had issues with Cox, if you use the forum search to look for Cox you'll find more threads.