Here's a few suggestions: Delete LW & LW's Preferences. Do a re-install of LW, do a
SAFE restart & Repair Permissions & re-install using the
standalone Java installer. This can apparently fix some issues with Java (See
slin's
post & link to standalone Java installer) And then install LW & do another safe boot. Some people have had problems after updating to 10.3.6
It's always good to repair your permissions with Disk Utility after a Safe restart both before & after you install software. Otherwise seemingly unknown errors can appear such as trying to launch the app.
Oh by the way, if you trash LW's Prefs you'll need to reset all your options/settings so make a note of them 1st. LW's prefs can be found here:
/Users/your_username/Library/Preferences/LimeWire