i was having connection problems as well, which started happening about a week ago after i've used limewire for many years without having any problems whatsoever. i did exactly what mick suggested. i uninstalled all my versions of java and limewire. i rebooted my computer. then i searched for any other files of limewire on my computer, i then deleted those, rebooted my computer once again. then i installed the offline version of the java (JDK5) and i installed limewire once again, and now it works! i am completely connected to the network and able to continue with my downloading needs. thanks for the help, mick.
hope it works for you all as well.