Mine computer is core2duo with 1gb ram & 128 mb onbord graphics card( 945 chipset family)
Please tell me what settings should I apply for nfs carbon to work. I have tried many combinations but in vain. So please help me.

Have you tried everything on lowest? Your integrated graphics card is going to be the big problem here.

You have a core2duo , but onboard graphics? Yuk

As far as NFS Carbon goes... it Won't work with your system. The CPU is PLENTY powerful enough. But graphics is to weak.

Minimum needed:
256MB Direct3D compatible video card
and DirectX 9.0 compatible driver

Do yourself a favor, purchase a dedicated graphics card. It will make a HUGE difference. You can get a PCI-E 512MB card for $50

If you post the exact make/model of your PC - and how much you want to spend. We can help you pick one.