same problem here, console dosen't record a thing on trying to open the application, but on re-instaling, the console was showing this-

Installing LimeWire 4.1.10 Pro. Java version is:
/Volumes/LimeWire/Install LimeWire.app/Contents/Resources/launchLimeWireInstaller: line 4: 727 Segmentation fault java -version
sw_vers is:
ProductName: Mac OS X
ProductVersion: 10.3.6
BuildVersion: 7R28
Copying /Volumes/LimeWire/Install LimeWire.app/Contents/Resources/Install LimeWire.pkg to /tmp/LimeInstallation/726
Checking Pro/Free

the bit that looks dodgy to me is this one-Segmentation fault java -version
any pointers?