Did you use the offline installer? You can get it at the link below. Also could you give us the setup of your computer. Is it a name brand or custom built. Also make sure your current version of java is uninstaled. Follow the instructions below.
First uninstall Java and LimeWire if you can then follow the instructions below.
You will need to go to Start/Run type regedit into the box this will open the registry editor
Go to HKEY_CURRENT_USER go to software expand it look for Java Script if you find it delete it. Now collapse it.
Now go to HKEY_LOCAL_MACHINE go to software expand it look for Java, LimeWire & Magnet delete them if you find them.Collapse it
Now go to HKEY_USERS go to S-1-5-21 the first one then go to software expand it look for java if you find it delete it. Collapse it. Close registry editor now go back to the original instructions and manually install Java then LimeWire.
Be careful when you are in the registry do not delete anything other than I listed above you can mess up your machine if you accidentally uninstall something or change your registry settings.
http://www.java.com/en/download/manual.jsp