Open Task Manager (ctrl/alt/del) & click on the Processes tab. Check if there's a LimeWire process running. If there is, end the process. Now, use your computer's search to look for all files & folders with limewire in the name & delete whatever you find. Restart your computer & see whether LW will install now. If you're still stuck, follow foolofthehill's advice here for removing all traces of LW.
http://www.gnutellaforums.com/283346-post2.html

Did you try to uninstall via Add/Remove Programs? That's the wrong way & can cause problems. Next time, uninstall via start > all programs > limewire & use the uninstall option from there. Also, installing a new version will automatically remove the previous version, providing you haven't tried to uninstall it another way.