have you tried these tips in the readme file that came with the game:
Troubleshooting:
* Civilization III requires OpenGL support. If you experience problems, make sure to download and install the latest drivers for your videocard and any service pack updates to your operating system.
* If you experience movie performance problems on Windows 2000, replace the binkw32.dll in the folder you installed Civilization III into with the binkw32.dll located on the CD in the \Bink\Win2k folder.
* Under Windows XP, you need to restart the game if you switch users accounts.
* Make sure your video card's hardware acceleration is set to maximum. The game requires DirectX 8.0a to run, and if this setting is less that full many DX8 features are disabled. To can access this setting from the Display control panel.
* Enabling Smoothed Screen Fonts: To enable Font Smoothing, open the Display Control panel, select the Effects tab, and check 'Smooth edges of screen fonts'.
* First edition versions Windows 95 did not include OpenGL, which Civilization III requires. A program named 'opengl95.exe' can be found in the root of the game's CD, which will install the required drivers. NOTE: This is only for first edition versions of Windows 95 that have trouble running Civilization III. If you don't have a first edition version of Windows 95 or you are not having difficulty starting the game, do not install these drivers!
* On Windows 2000, if you experience any problems with fonts or text, make sure to download and install the latest service pack available for this operating system. You can find the latest service pack at
www.microsoft.com.
I recommend enabling the font smothing thing.