Ack... Maybe I'm just stoopid, but what solved the problem for me was (once again) uninstalling Java (via the Add/Remove Programs applet in the Control Panel) and reinstalling Java ... BUT ... This time I installed the JDK version, NOT just the usual Java Runtime Environment (JRE). Reinstalled LW and, voila!! Problem solved!

Maybe it's been made clear elsewhere, but I don't think most users would install the JDK verison of Java unless explicitly told to. I certainly didn't think that's what was required, but it appears it may be.

Top download on this page, the J2SE(TM) Development Kit 5.0 Update 11.