My graphics card -- a Geforce GTS 450 -- came with a chord meant to connect it to a power chord from the PSU. It's connects to the GeForce using a black six-pin male connection, then branches into two sets of wires that each terminate in a white male connector with four holes, three of which are filled with wires.
Can anyone help me identify this so I can buy a new one?
Honestly, you shouldnt be using it anyway, your PSU should have a single PCI-E connector that can plug straight into the card, what you broke was a 2 molex to 1 6 pin PCI-e adapter that is meant to work around systems that have PSUs that didnt come with a PCI-e connector but if you read the manually i bet it will say that the use of the adapter is recommended against.
What is the make and model of the power supply unit? If it doesn't have a 6-pin PCI Express supplementary power connector it may be weak on its +12Volt rail or the power supply unit was only designed to handle graphics cards that required less than 75 Watts of power.
If you have a minimum of a 400 Watt power supply with a +12 Volt current rating of 22 Amps and with a minimum of one 6-pin PCI Express supplementary power connectoryou should be fine.