I've had very much the same problem - brand new computer running vista with 2gb ram, dual core 2ghz processor, SIS672 Mirage chipset and some crazy graphics.
Updated to the latest drivers, patched Civ to 1.74, got the latest Direct X drivers and yet the problem persists.
I'd describe it as the different graphical layers appearing and disappearing, as if it was cycling through them, plus some artifacts across the screen. Yet each 'layer' looks fine - for instance, the map is pretty constant and renders fine, no texture problems, but things like the actions menu (go to, auto explore etc) are only there some of the time, flickering on and off, and messages jump around the screen in a bizarre way.
Unfortunately I don't have access to a copy of XP so can't install it myself, anyone have any ideas what can be done?