T3600 with GeForce GTX 780 Ti crashes

I bought a new Dell T3600 workstation with 635 watt power supply and separately an Nvidia Geforce GTX 780 Ti. I have some issues with it.

The card requires an 8 and 6 pin PCIe power connector. The T3600 however only has two 6 pin PCIe power connectors.

Still, under extreme loads of the graphics card (3dMark 11 or furmark for example) my system instantly reboots with no error message whatsowever. My graphics card requires a 600 watt power supply so it should be within limits. But is it? When I use a power meter my entire system uses only around 300 watts when running 3DMark which is nowhere near the PSU's limits.

Can anyone help me?