What was your previous version of LW?
1. I'd recommend you remove your java in case it is corrupted & reinstall. See Point #1 here
Fixes for Limewire (click on blue link) & only choose the OFFLINE download option.
2. Do step 2 or 3 in above link depending which is applicable in your case.
3. Go to Start menu -> All Programs -> LW -> Choose uninstall.
Then get this version ->
Download ‘Other’ version & simply unzip & use!