Try a safe boot & repair permissions.
Reboot whilst holding down SHIFT key until you see a window saying something about safe booting. Choose yes. Safe booting takes much longer than a normal restart. After it's booted up, go to Utilities folder & open Disk Utility. Repair permissions. Then reboot normally. Hopefully LW will be working fine after that. If not, see below.
Have you seen this?
QuickTime 7.0.4 bug stops LimeWire from opening!
Make sure LW is using Java 1.5 & not 1.4.2; see
Setting up Java 1.5
If this is not your first try at using LW, then also try deleting the LW preferences folder found here: /Users/your_username/Library/Preferences/LimeWire