Regular GDI/GDI+ graphics is HW accelerated, whenever possible, through MS/Intel/AMD co-operation in developing the Windows OS' stock drivers. Neither nVidia nor ATi have any relation to this process.
2D and 3D acceleration is a specialized field that requires dedicated GPU design, and this is where the both brands step in leaving Intel and Co.'s general-purpose products far behind. Both of them predominantly use OpenGL as their development platform and target, and they condescend to MS' DirectX competition to OpenGL only insofar as MS is what it is and because it also has its own, though minor, game console platform in the form of xBox. Surprisingly, gaming has always been one of the major factors in the IT industry's speedy progress towards smaller geometries and faster HW.
To enjoy the benefits of HW acceleration, you should accept the rules of the game: use dedicated graphics libraries/engines/environments (OpenGL/WebGL or DirectX) and languages (GLSL or HLSL) to develop your graphics routines and entire applications, rather than rely on occasional MoveTo()/LineTo() and turtle (literally and otherwise) graphics tactics.
