graphics card affect performance?

I executed my drawing program on different types of pc, and on one pc, the program will hang halfway when ran, is this because the graphics card is not powerful enough?

The title of your topic should read “Graphic card may affect stability ?”
It may be the case, but it is more often due to buggy drivers. It can be a heating problem (GPU/videoram/CPU/RAM), an overclocking problem (same candidates), a faulty component such as buggy ram, etc.