A:
Unfortunately, there is more than one DVI socket in existence. there is the DVI-D and the DVI-I. I ran into the same problem with my Laptop. It sounds like your new cable is a DVI-I and the socket on the back of your computer is a DVI-D.
Here is the difference:
DVI-D only transfers Digital format signals
DVI-I will transfer Digital and Analog signals
Now that you know what the two sockets are and what they do here are my solutions:
One, try to return your DVI-I cable to find a DVI-D cable to VGA cable.
Or
Try removing the for pins that are above and below the copper bar [on the left side] as they are meant for Analog transmissions and don't matter for hooking up your PC.
Not sure if you have single or double DVI(s) so I uploaded both pictures
Best of luck!