Hmm I've heard of that problem before. Go to add/remove control panel & remove all earlier versions of Java & just leave the latest version. Then reboot. Download the "other" LW installer version & try that.
Download ‘Other’ version & simply unzip & use!. If still issues, try the options here
Fixes for Limewire
Not sure what you mean from your old computer. If you want to transfer your previous incomplete files, copy the entire incomplete folder from the ME machine & replace the new incomplete folder on the XP machine but ONLY whilst LW is closed & of course after you have successfully installed LW.