Well, I'm not sure why setting the background-color property to #FFFFFF isn't stopping the transparency (I'm assuming when you tried everything, this is what you did).
Looking at your source code, this appears to be a pretty standard nested list structure with CSS flyouts. I notice you're using the PixioPoint Multi-level navigation plugin. I don't use this plugin myself, but did you try to use their style sheet creator, found here:
It looks like this will let you tweak your plugin style, and hopefully turn off the transparency.