How do I fix this so that I can play my game. My kids deleted several programs without using uninstall and this is the only one that does not work after re installing.

here is an image of the error. Windows 8.1

Solved! Just needed to remove the registry keys associated with the game and a couple temp files.

How did you do this? I am having the same issue.

Here is one way to do that. A fair warning, tampering with the registry can break other programs or Windows itself...

While you can delete the registry entries manually, its not recommended as you might break something important:
Revo Uninstaller should allow you to remove all of the registry keys when you remove a program. After opening Revo, select Alpha Centauri from the list of installed programs and uninstall it through Revo. It will then run Alpha Centauri's uninstaller. If it fails, don't worry. Revo will then offer to clean up any remaining files and registry entries. Chose to select all and delete at each step.

Removing the temp files is easy. Run the Disk Cleanup utility, make sure Temporary Files is checked and delete.

Strangely a computer restart solved the issue.Never had to do that in AC before.