The laptop screen resolution probably is the problem. That resolution really isn't suitable for running games. Try the following:
1. Add the line DirectDraw=0 directly beneath the [Alpha Centauri] line in your ini file. This will attempt to force the game to run at your native Windows resolution (1024x600). This would be the best you could hope for, but may not work. If that doesn't work, then
2. Remove the DirectDraw line and replace it with video mode=800. This will attempt to force the game to run at 800x600. Assuming that your laptop supports such a resolution, this probably will work.
(Be sure to edit the ini file with a text editor such as Notepad. You may have to run Notepad as the Administrator, even if your user account has admin rights.)
HTH
Petek