Is there any listing of LimeWire on the computer? If yes, check to see if there is a LW menu in Start menu > Programs > LW & look for uninstall. Otherwise check Remove programs control panel. Then run the Crap Cleaner program listed above.
Now, install Java:
Download Java software from Sun Microsystems (choose only the offline installer, after downloading you can install it .. it's about 15 MB download size.)
Then download this version:
Download ‘Other’ version & simply unzip & use!