The problem is that I have never heard of a similar situation. I doubt this is a problem in Limewire or in Java, but you could always try to download java 1.5 and downgrade LW to a prior version
http://www9.limewire.com:82/download/ . If that combo doesn't work and Cox tell you everything should be working, that might be an issue with your specific machine. In that case stick to P2P that works for you