Hmm, maybe some Security Program blocking LW from writing the registry keys...
Disable all and try again.
Maybe changing the compatibility mode might also have an effect. Right click the exe icon, go Properties>Compatibility and change it to Windows NT (or Windows 2000)

Last but not least you could reboot in Safe Mode and try to install LW then.

Do you have Java preinstalled using the JRE offline installer? If not you need also to consider to uninstall LW and all Java versions on your system. Reboot and then download the JRE offline installer of the newest Java version from here:
http://java.sun.com/j2se/1.5.0/download.jsp
Install it and reboot again, then reinstall LW.

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"Never Argue With An Idiot. They Will Drag You Down To Their Level, Then Beat You With Experience"