Have you recently updated Java? Some people have had this problem with LW not opening after updating to Java 1.6.0_01 & _02. Try this version of Java instead. Use the JRE offline installer & remove your current Java version(s) before you install this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

Next, delete 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 kill 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 LW's still not opening, try changing compatibility (point 5 in the 'fixes' thread).