You could also try question in windos 7 forums.
If you have not, you can run Dxdiag from Run command that is made available in rightclick taskbar->Properties.
or you can find dxdiag.exe in \windows\system32. This may show otherwise unknown problems.
your issue is not with directx version likely it's that those games require a shader version or the likes to run
and your video card being intel onboard is what one would call a 2-1/2d card rather then a card able to play advanced 3d games
if I were you I would be looking at the forums for the games that will not run if there is some way to manually lower the visual settings even lower so it works on intel hd 3000
any windows laptop with the same onboard video card would have the same problems as you