You'll have to use crlt&alt and press one time "delete" to open your Task Manager. There you go to the Processes tab and check whether there is a limewire.exe running. If so you'll have to force it to end. Then try to delete LW using START>Programs>Limewire>Uninstall......
If that doesn't work (because you've actually removed the program already via the "Remove Programs" function of the Control Panel) you'll have to use the search function of your computer (START>Search...>For Files and Folders....) using "limewire" as search query to find all remaining files and delete them manually. Then you restart your computer and try to reinstall LW using the offline installer.
Make sure that you have prior to the LW installation your Java updated. To do so, remove all Java versions from your system, reboot, download the JRE offline installer of the newest version (1.5.0_08), install it and reboot again.
You can get the newest version here:
http://java.sun.com/j2se/1.5.0/download.jsp 