The issue may not necessarily be the newer apple computers. Try these things:

1. Try reinstalling your Java using the "Offline" Java installer. I think the most recent one for Tiger is this one: Java 1.4.2 for Tiger (click on link) If it doesn't let you install it because it says it's already installed or the installer give a "Null" error, then go to the Receipts folder & delete the last Java package. See similar example here (this example is for Panther so the version will be different): Receipts folder sample image
* * * However, check which version of Java you have. IF you're using Java 1.5, then you should get this installer Java 1.5 Standalone installer Also if you have Java 1.5, go to your Utilities folder & open the Java utility. Set it to allow LW to use it. See notes about this here: http://docs.info.apple.com/article.html?artnum=301073

2. Normally after installing new software or updates including system updates, you should repair permissions. Reboot your comp whilst holding down the SHIFT key until you see the window saying Booting into Safe mode or similar message. Then after it's finished booting, go to the Utilities folder, open Disk Utility & Repair Permissions. Then reboot back into normal mode.

Tell us if these things make any difference.

Edit: Ok I hadn't seen this thread. Perhaps you hadn't either but please try the 2 suggestions above anyway. iMac Intel Core-Duo Limewire Does Not Open?!?!?!