Well, I hate to admit it, but I also have a Powerbook G4 running Mac OS 10.3.9.
I had the exact same issue with Limewire quitting at startup. I followed the Limewire links to the apple website, and I found I did NOT have any of the java or other possible problems.
I went to:
http://www.mager.org/LimeWire/
and this solved my problem as well.
I feel bad getting a "bogus" version, but this is the only way I've been able to get Limewire to run.