First of all, reinstall Java again (sorry) & make sure to use the JRE offline installer. Remove your current Java version before you install the new one. You'll find a link for downloading Java in point 1 of the thread here
Fixes for LimeWire

Next, delete LimeWires preferences folder when LW's properly closed (check in task manager to make sure it's not running). The instructions for this are in point 3 of the thread above. It's not hard to do but make sure that you've got hidden files & folders showing...the folder's hidden by default.

Now reinstall LW & make sure to use the offline installer (not the recommended one). No need to uninstall the version you've got now...it will be removed automatically when you install the new version.
http://www.limewire.com/english/content/download.shtml

If none of that works, then try changing compatibility. The instructions for that are in point 5 of the 'fixes for LW' thread.

If it's still not opening, maybe you have some security program that's causing a problem? Make sure that LW is on the list of exceptions/allowed apps for any antispyware programs etc that you might be using.