Even at the low level, very little of the Windows GUI is hardware accelerated. The Windows cursor is probably the only part you see. Basically everything else is done by drawing into a frame buffer without any hardware support at all. There are a handful of low level graphics primitives that can be hardware accelerated, but few of these primitives are commonly used ones.
This is why the market for 2D video cards died, they had all put everything that Windows used in hardware, and had all reached the limit of resolution that anybody could actually use, and where all faster then Windows could keep up anyway. Thus price and odd ball features like TV-out became the only way to differentiate 2D video.
Part of the problem is that the Windows repaint architecture is very crude. It was designed for systems with very dumb video cards and very limited memory. Thus it doesn't try to do anything clever, nor is it setup to take advantage of any abilities that the hardware would provide.
When Windows first took off, there where actually special 2D video cards that had abilities that windows didn't use. The one I remember off the top of my head is that some video cards had build in hardware scrolling rather then the software level used by Windows even today.
Jay