I recently deleted some files files from Limewire to the Recycle Bin and later tried to restore them to LimeWire but they are gone. Where do restored files go from the recycle bin?

well that depends, are You using Vista or xp? The best way to find it is do a search for one of the file names. ie. start-search in xp, or start-type in file name select search everywhere in vista. When found,right click and open Containing folder. remember where it is located.