If you've tried updating Java, deleting preferences, changing compatibility & reinstalling LW...make sure that you're not having a conflict between a security program & LW. Are you using any antisypware or security programs that might be seeing LW as a threat & so not allowing it to open?

Make sure that LW's on the list of exceptions/allowed apps of any antispyware etc.

Is this a new problem with an experienced user, or is this your first try with LW?