HD 6850s should only be having a single PCIe power connector slot. Is yours a OC'd one or so? I'm not sure why this one requires two though...
You might need to upgrade your power supply in order for that card to run.
Here's one for $50 after mail in rebate.
It's got 2X6 pin PCIe power connectors, and should be enough to run that HD 6850.