Try deleting your LW preferences folder, see points 2 & 3 here
Fixes for LimeWire

Has LW ever worked or have you just downloaded it? You could also try removing your current version of Java & reinstalling, using the offline installer (there's a link for that above).
Try changing compatibility to Win 2000 or NT.

Are you using any antispyware? Some will see LW as a threat & will stop it from opening. If this is the case, make sure LW is on the list of exceptions/allowed apps. If all else fails, disable the antispyware & see if LW will open