I don't know why LimeWire's not running for you. What system are you using and how did you install it?

However, from your path statement it seems as though you have the JDK and the JRE installed. You only need one or the other. The JDK includes the JRE. Since you have the JRE 1.3.1 and the JDK 1.3.0, I suggest removing the JDK.

If you want to write java programs yourself, remove the JRE. Ideally you'd want a 1.3.1 JDK but you may be able to get away with the 1.3.0 version.