Does Call of Duty run on a 128 MB ATI X1250 graphics card?
There a service called CanYouRunIt from System Requirements Lab. It will automatically analyze your computer in just seconds, and let you know if you can runthe game on your PC.
MakeUseof Review: http://www.makeuseof.com/tag/muo-games-analyze-your-computer-for-game-compatibility/
direct link: http://www.systemrequirementslab.com/cyri/
for which game in the Call of Duty series are you asking? Call of Duty 1 or 2 will probably run with your card. The other ones require more than 128MB graphics memory.
I guess this is 128MB shared memory? How much RAM do you have?