1. What I'd suggest is
SAFE Boot & Repair Permissions
2. Delete the LW Prefs folder found here: /Users/your_username/Library/Preferences/LimeWire
* If that doesn't fix it, create a new virgin account. Then try opening LW from that account. If it doesn't work, then it looks like probably a problem with the java. I think there was a reasonably recent Panther security update (I rarely use Panther now) which may have mucked up the Java. Else something else has affected it.
System Preferences -> Accounts -> click the padlock & then put in your password in the window that appears. You will then see option to add or remove accounts. Press the
+ to create a new account & name it something like Test. A window will open giving you options to name the account, a password, etc. After doing that, log out, then log into the new account & try to run LW.
If LW doesn't work then it looks like a re-installation of Java is needed (question is which one.) Let us know how you go.