Try to check whether there is a Limewire process running in your task manager (press "crlt&alt and hit the delete button once, then go to the process tab). If there is, force it to stop.
If that doesn't help, go and search for all limewire files on your computer via START>Search>Files and Folders. Delete them.
Then you open your registry via START>Run and typing regedit. There you go to Edit>Find and search for all limewire keys with the search query "limewire". Delete all you find.
Then restart your computer and reinstall LW.
If that also doesn't solve your problem, then you have to uninstall LW again and also all Java version on your system.
After having done so, restart the computer, install Java using the JRE offline installer, then reboot again and reinstall LW.