Actually I understand that this is not certainly a bug, but maybe You could give me some hint / propose some workaround. By experience most of the games work no problem with 16MB of graphics memory at 1024x768 16bpp.

When I executed the game for the first time it gave me a notice that it might not work with my card since it has less than 32MB of memory.

The specs of my laptop (in case You find it helpful):
IBM (Lenovo) Thinkpad X31, Intel Centrino 1.7GHz, ATI Radeon Mobility M6 LY (aka Radeon Mobility 7200), 512 MB RAM...

here is the debug information:

Debug Message: *********END dxdiag info.*********
Debug Message: Entering WinMain
Debug Message: ******* Starting Game Shell *******
Debug Message: Going Fullscreen
Debug Message: Preparing to change display settings.
Debug Message: Multisample Type chosen in prefs not supported. Forcing a supported type.
Debug Message: Using multilsample setting: D3DMULTISAMPLE_NONE
Debug Message: Game Resolution: 1024 x 768
Debug Message: Running fullscreen.
Debug Message: HAL (hw vp): ATI MOBILITY RADEON
Debug Message: D3DPRESENT_INTERVAL_DEFAULT
Debug Message: Refresh rate: 60
Debug Message: Bit Depth: 16 bit.
Debug Message: *********Checking D3DDevice Caps***********************
Debug Message: A full-color cursor is supported in hardware at high resolution modes.
Debug Message: RGB in format 5:6:5, Masks reported as f800:7e0:1f
Debug Message: Now Fullscreen
Debug Message: Shell initialization complete
Debug Message: ***** Initializing Game *****
Debug Message: Timer Frequency is 0 369e99
Debug Message: Initializing sound card.
Debug Message: initailizing bink
Debug Message: Create setup screens.
Debug Message: Clear galaxy settings.
Debug Message: Clear influence.
Debug Message: Clear up laws.
Debug Message: Clear first time events.
Debug Message: Clear wonders and trade goods.
Debug Message: Clear sector mapper.
Debug Message: Set mouse.
Debug Message: Set update timer.

Please help, can't wait to put my hands on the sequel
Best Regards

Iwo Zmyslony