Since without JS there is no change in image at all, my personal preference would be to CSS this and then add a little itty bitty JS to change the time (so you get the fade stuff).
However that aside, I wonder if its this:
I can't read jQuery but I would assume the .hover method of a DOM element would follow the same rules as element:hover in CSS. That means you are looking for the event of :hover on a li element which IE6 does not understand.
HOWEVER you have the suckerfish JS which DOES help IE6 understand what :hover on non-anchors means.
So, I don't know this but if I were given this as a little Rubix cube to play with, I'd see if IE6 magically worked if you switched the order of the scripts in the <head>. What if IE6 is first told how to :hover over non-links and then is told to Do Stuff on div#button li.hover?
BTW (off topic) I don't have Flash installed but I see you has a flash... have you checked that the dropdown menu at the top always sits over the Flash in all browsers? Just wondering, I can't see if there is a problem without the Flash player.
Oh and another thing: in Firefox the black page container does not enclose the right sidebar, and text is sitting over images and spilling out everywhere. This may be a work-in-progress page but if you weren't aware of it, I'm letting you know. http://stommepoes.nl/alite.png