I had posted to these forums a solution to everyones' ails (no complaints or disagreements so far) and I will repost my solution to this thread.

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I get this when I do java -version:

java version "1.3.1"
Java(TM) 2 Runtime Environment, Standard Edition (build Blackdown-1.3.1-02b-FCS)
Java HotSpot(TM) Client VM (build Blackdown-1.3.1_02b-FCS, mixed mode)

Make the appropriate changes depending on where you installed your java installation whether it be sdk or jre:

I put where I downloaded my j2sdk1.3.1-02b-FCS:

/usr/lib/j2sdk1.3.1

into my PATH in my .bash_profile:

export JAVA_HOME=/usr/lib/j2sdk1.3.1
export PATH=$JAVA_HOME/bin:$PATH

After doing that, I remove kaffe from my system but I have a dependency problem with my wizard packages. I do this command to keep that program around:

rpm -e kaffe --nodeps

This removes all instances of kaffe binaries from /usr/bin.

I next create soft links to the /usr/bin directory but blackdown has most of all of it's java commands (ie java, javac, etc) as symbolic links. Some people´s configuration will not allow that many symlinks.
the symlinks point to a "hidden" file called .java_wrapper. So I link this to my /usr/bin directory like so:

ln -s /usr/lib/j2sdk1.3.1/bin/.java_wrapper /usr/bin/java

After doing that, I execute the LImeWireLinux.bin installer (do this as a regular user and not root. I don't know a way to install it system wide as root yet without making a script.):

./LimeWireLinux.bin

Installation works. Program installed, running, and functional. I discovered that I had to install the program as user instead of trying to set it systemwide as root.