Make sure to use the offline...less chance of any corruption.

Try this way & see whether it installs & loads properly:

Install Java first. You can either update to the latest version here: Java SE Downloads
Or, if you have problems with the latest update, try this older version, which has worked well for lots of people:Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11 (if you've already tried the latest Java, give the older version a try & see if that changes anything).
Whichever Java version you use, download the JRE offline installer & remove ALL OTHER JAVA VERSIONS (via Add/Remove Programs) before installing another one.

Next, download the LW 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 you're still stuck, try using the 'other' installer. Click on the link below for info.
Installing using the 'other' installer