The reason Limewire does not open appears to be the latest JAVA release jre1.6.0_01. Have no idea why but that's the culprit. After I installed that Java release, I started having problems opening Limewire.
I removed that JAVA release and was able to open Limewire, however I had other problems occuring and Limewire didn't really connect, so for now I've re-installed the new JAVA release again. Not sure what I will try next.