Broken connectors / pins on graphics card

What you’re seeing is actually not a broken connector. These pins are intentionally kept short so they connect last. Remember that PCIe is hot-plug capable, you can add (and theoretically also remove) cards in a running system. If you look inside a USB plug, you can see something similar: The data pins are shorter than the power supply pins.

The short pin near the rear of the card is “PRSNT2#”. The one to the front is “PRSNT1#”. It’s connected to the rear pin and informs the motherboard of the length (in PCIe channels) of the card. There are multiple possible “PRSNT2#” locations, one for each possible card length.

You can read more on the PCIe connector on Wikipedia.

Stackcraft_noob is right about bad connectors that can damage your system, however, he is wrong about this case. NOTHING is wrong with these connectors, as Daniel B states, this is how they are manufactered. It's (almost) always the first pin from the right on the back, and the second pin from the right on the front.

As you can see here:

And here:

Just google any recent graphic card from AMD or Nvidia, and you will see all cards have this. If you see a card that has not, you are looking at a render.