I am not quite clear ... are you going from one Mac OSX 10.3.9 to another with the same OS? Also are you upgrading to a different version of Limewire?
Sometimes it is better to keep the old version, just in case the new one gives you problems, just until you know you are happy with the new one.

If your sure you want a fresh install:I would get your new limewire from www.limewire.com.

To uninstall go to applications, drag the limewire folder to the trash. Also go to users>your name> library>preferences>limewire and drag that to the trash .... That's it. Somewhere you might have a installation file LimeWireOSX.dmg you can search fot that and delete it aswell, if you still have it. Macs tend to get cluttered up with them... mine does anyway!

If you particularly want to keep the preferences I suppose you could copy them to the new computer, but It is probably better to reconfigure the new Limewire.

I hope this helps. enjoy your Mac!

__________________
To get Phex Click on the Fox