Go into task manager (ctrl-alt-del) & see if any LW process is running. If it is...end the process.

Go start > all programs > limewire & use the uninstall option there to remove LW (if you get an error here, let us know what it says).

Next, install Java using the JRE (Java Runtime Environment) offline installer. Go to add/remove programs & remove your old version of Java before you install the new one.
http://java.sun.com/javase/downloads/index_jdk5.jsp

Now reinstall LW & make sure to use the offline installer, not the recommended one (fewer corrupt installation problems with the offline installer).
http://www.limewire.com/english/content/download.shtml