I think I might have sent you down a dead-end. It seems that you have the latest graphics driver available for your computer:
http://www.dell.com/support/drivers/us/en/19/Product/inspiron-15-intel-n5040

I think you should follow mistermumbles advice and try to modify the dosbox config file in the game directory. For Dragonsphere, the file is called "dosboxDragonsphere.conf" and try to set output=overlay or output=opengl.

Have you tried contacting GOG support yet? They're generally pretty helpful. (Point them to this thread, too.)

Try installing it to another location, e.g. C:\Games or C:\GOG.

Windows 7 can be a bit funny with permissions on the C:\Program Files folder(s)...