Bonnie / Bob,
A colleague alerted me to a potential drawback with the Intel GMA 965 you mentioned below. I've just been looking into this: if it is the "Mobile Intel(R) 965 Express Chipset Family" the Intel website indicates this only supports OpenGL 1.5 rather than the later OpenGL 2.0 required for ArcGIS Explorer (http://www.intel.com/support/graphics/intelg965/sb/CS-023713.htm).
I don't believe a driver update would move the support up to 2.0 but it's worth trying anyway. You could try checking for a more recent driver: http://www.intel.com/support/graphics/detect.htm.
The Intel website also says "Also, exit any running background applications or programs that run in the Windows task bar".
Regards
Mike