Try deleting the LW preferences folder, see points 2 & 3 in the link below
Fixes for LimeWire
Uninstall your current version of Java & reinstall JRE using the offline installer, see point 1 above. Did you reinstall LW using it's offline installer? If not, try that
http://www.limewire.com/english/content/download.shtml
If you're using any antispyware programs, make sure that LW's on the list of exceptions/allowed apps. Some antispyware will see LW as a threat & prevent it from opening or running. If in doubt, try disabling any antispy & see if LW will open