Hi Ignus,
Welcome to the forums! Sorry to hear about your troubles here, but it sounds like some sort of driver/settings issue with your graphics card in this case. The menus in question are GDI-based (that's the native Windows graphical interface), whereas the other parts of the game that are working fine are DirectX-based.
Generally speaking, GDI is not known for being hardware accelerated, mostly that is handled in software on the CPU. However, a lot of the decisions for that are in the windows/driver layer, so decisions for that sort of thing might fall under the purview of a driver; not positive on that. So it's possible that the new nVidia drivers are doing something new with trying to hardware-accelerate the desktop, and this is causing the issue.
My suggestion would be to rollback to a prior version of the graphics driver (there are places you can find those online if you don't have them on your PC), and see if the problem goes away. If so, then most likely this is just something bugged in that version of the drivers, and probably that will be fixed in another version or two. Seems like there are always little things breaking and then being fixed with various games with each new version of a graphics driver update, although this almost never affects AI War since what we're doing is more vanilla. But it does happen.
If a graphics driver rollback doesn't solve this, then something else unusual is going on with the GDI render pipeline. Could be an assembly of .NET 3.5 that is messed up and needs to be reinstalled, or it could be something else. The fact that you are only seeing this in two games, and not in dropdowns elsewhere on your desktop, is curious. That sort of smearing and blanking behavior is classic GDI behavior when the UI thread is too busy to actually render anything, but I don't know what might have changed in a driver update to cause that.
Hope that helps, at least! Please let us know if you find out any more info.