Have you made sure to use the offline installers for both Java & LW? Online installers can sometimes have problems with corruption occuring. If you didn't use offline installers, start from scratch again (sorry).

Install Java first. You can either update to the latest version here (I have this one & LW's working fine): Java SE Downloads
or try this older version, which has worked well for lots of people: Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11
Whichever Java version you use, download the JRE offline installer & remove any other Java versions installed on your computer before installing another one. After installing Java, restart your computer. If you have more than 1 Java version on your computer, that might be causing problems.

Next, reinstall LW & make sure to use the offline installer. When you click to download & a dialog box pops up, cancel it. Now use the option to download the offline installer
Lime Wire » Download LimeWire

If that doesn't help, try deleting LW's preferences folder when LW's properly closed. See point 3 here & also point 2 if you've used older versions of LW in the past (there could be a folder in either location).
Fixes for LimeWire
This will change all of your settings within options, you'll have to go back through afterwards & reset things. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.
You'll know if you deleted the preferences folder properly - when you start LW, it will go through the setup wizard again.

For old versions, try here.
Old Version of Limewire Download
If they don't have the version you're looking for, send me a PM. I have a few old versions saved.