Your bottleneck probably isn't the processor or graphics card, since that i5200U model you mentioned should be more than powerful enough to run Cave Story, and any computer that has that kind of processor probably has more than enough memory to run Cave Story.
You mentioned DXGL in the thread title. I'm not too familiar with what that is, but based on a cursory Google search, it looks like some kind of alternative to OpenGL. If there was some manual change you made to the graphics libraries that your OS uses to run games, then you could try un-doing those changes.
I guess another question is, are you running the original Cave Story, or are you running a NICALiS port? Seems like your computer should be powerful enough even to run CS+ smoothly, but you never know.