I've had Limewire for a while now, but have recently been having trouble with it. When I click on the desktop icon it comes up for a split second and then closes and does nothing. I followed a lot of directions given on this site but nothing seems to help. I did manage to find the Limewire Executable Jar Icon under my program files and the program opens when I click it, but it doesn't open when I click the desktop icons. Can someone help me figure this out?

Have you recently updated your Java version? Some people have had this problem after installing Java 1.6.0_01. If that sounds like you, try this Java version instead. Use the offline installer & remove your current Java version before you install this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

If that doesn't help, 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.

You could also try changing compatibility (point 5 in the 'fixes' thread).