Try deleting LW's preferences folder when LW's properly closed. See point 3 here & also point 2 if you've used older versions of LW in the past (there could be a folder in either location).
Fixes for LimeWire
This will change all of your settings within options, you'll have to go back through afterwards & reset things. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.
If you're using Vista: LimeWire Pref Folder in Vista

If that doesn't help, right click on the LW icon > properties > compatibility. Try running in compatibility mode for Win 2000 or NT. If using Vista, try compatibility mode for XP.

Do you have Alcohol software installed? If so, look here.
LW starts then close, log: resolve_virtual_call

Did you remove any other Java versions on your computer, before installing the latest version? If none of the fixes above work, see whether this older Java version makes any difference. Download the JRE offline installer & remove any other Java versions before installing this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11