In response to your personal message, delete the installimewire.pkg file from your receipts folder & try installing again. Receipts folder sample image. Also make sure you deleted the previous LW prefs folder.

Also see if you can find any limewire crash reports. This will hopefully show why LW is not working on your system. Else ...
Console is in your Applications folder inside the Utlities folder.

Could you open Console, and then try to open LimeWire, and then note what messages are shown in the Console?

You can post the parts here, or PM me if you prefer.

I don't have such an intel-mac so I can only advise as to what usually causes this problem.