Activision has released a small patch for Star Trek Starfleet Command III. The patch allows the game to "properly detect later versions of DirectX and enables it to play on systems with DirectX 9 installed." Source: 3D Gamers.
Gamer's Hell Local Download:
Star Trek Starfleet Command III by Taldren - retail DirectX 9 fix
This download allows Starfleet Command III to properly detect later versions of DirectX and enables it to play on systems with DirectX 9 installed.