Unistall all 3 Java and Limewire. If it asks you to reboot after each uninstallation do not restart just uninstall all 4. When done uninstalling, reboot your computer. Download Java Runtime Environment 5.0 Update 4.

Use offline installation

Some people may have Update 4 and it may not be working.

Download JRE Update 3

Use offline installation

Reboot you computer.

After starting back up, install Limewire 4.X.XX.

After finish installing limewire. On the last screen of the installer, it will have a checkbox. If it is checked uncheck it.

Now try running LimeWire from the desktop.

Also try what Lord of the Rings was saying. Try scanning your computer for possible infections of spyware, malware, adware, viruses. There is also a worm called W32.P2P-WORM.ALCAN.A
that might be messing with you.
Ad-Aware will detect this but may not remove it properly.
HijackThis will probably detect it, but I don't know.
Also if you have Comcast High Speed Internet, there is free McAfee VirusScan, Personall Firewall +, and Privacy Service offered to you by Comcast. You will nedd to have a comcast email address to do this. Such as xxxxxxxxxxx@comcast.net. Click for Mcafee & Comcast page.