Do you mean that the Displayport cable isn't fitting into the Displayport slot on the video card? Are you sure that you're plugging it into the right slot? A Displayport slot and an HDMI slot can look very similar, but you have to make sure that you don't mix them up because they are not compatible.
The cable shouldn't shift if you are plugging it into the right slot properly. If it is shifting and you are sure that you tried usign the right slot, then yes, something might be broken.