Try SAFE Boot & Repair Permissions first.

If still problems, then see Can't launch LW: Bouncing in Dock (click on link).

My guess is you may have Java problems if repair of permissions doesn't work. Reinstall Java from the mac site using their Offline Standalone installer. Offline installations are more reliable than those via mac updater.

Something else you can try is set up a different test account, see if LW works in that account. Setting up a Test Account in OSX (click on link)

As for firewall, if you still have the brick showing after you can eventually open the program, then if OSX firewall is on, put LW on the safe list: OSX Firewall settings for Tiger

If still a firewall (brick icon) after that, try to find the brand name and model number of your modem/router and post the detail back to us.