Currently, there are close to nothing but problems in D3D mode, as far as I know.
What I would do is to first try OpenGL with different builds of FS_Open, and if the OpenGL mode still didn't work, I would try to install either newer or older drivers for the graphics card and try the OpenGL mode with different driver versions. If it still didn't work, I would only then turn on the D3D.
As for D3D, I don't think it has been actively supported in a while, so the latest mediavp's for example will quite likely cause bugs like the white cockpit glass and stuff. If you have to use D3D, get an older build and older media_vp's, they *should* work...
I don't understand why OpenGL shouldn't work on your laptop.