some of it
Your java is not working (google "buckyball")
Shut down, wait two minutes, restart, then as soon as you hear the startup tone, hold down the shift key. Once you see the grey spinning cog, you can let go.
This is called "Safe Boot mode" and will do a file system repair and check.
Then run Software Update from the Apple Menu.
Repeat until software update says you are up to date, and don't do anything else until complete.
Then run Disk Utility (in your Utilities folder), click on the hard drive icon in Disk Utilities list, and select Repair Permissions. Let it run and don't worry about a dozen or so messages printed there.
Do another safe boot
Do a regular restart
Delete all LimeWire folders, installers, and then go to
http://www.mager.org/LimeWire/LimeWire.html and use the http link to download the LimeWire CVS build (4.9.32jum433) with Safari
Open the .dmg and follow the instructions.
It should work now.
[Hobo--that DIX program is rather neat, but not for removing duplicates. Thanks to your son for the link; sounds like an intereting developer]