The picture you posted is a MOLEX connector. Since you say it is coming from your graphics card, it must be the case that your power supply doesn't have the necessary PCIe power connectors. The MOLEX connectors would connect to disk drive power connectors. You may not have any of them free.
You will need to look at the power supply and reply what the wattage is. My guess is that your power supply may not be enough to support your new graphics card.