Your description best fits a short circuit on a power rail.
It could be a bent CPU pin, or a shorted peripheral like a HDD or DVD drive but a red flag goes up when you say 4 pin power connector.
Many power supplies have a 2x2 (4pin) plug for a video card as well as a 12 v plug for the CPU power.
Both plugs are 12v, however, the 4 pin video is reverse polarity of the CPU plug. .Plugging it into a CPU power socket is a direct 12 short to ground.
Pg 23 of the user manual shows the correct power plug requirements.http://download.gigabyte.us/FileList/Manual/mb_manual_ga-z68a-d3h-b3_e.pdf
Corsair FAQ mentions:
Our power supplies ship with an 8-pin connector that splits in half. Use half of this connector for the 4-pin EPS/ATX 12v connector on your motherboard.
and lists 2- PCIE power connectors which would be wired wrong if you are somehow using one of them.
ATX Connector 1EPS Connector 1PCI-E Connector 24 Pin Peripheral Connector 4
You could try with out the 4 pin connected to see if you get error BEEPS or even try without the CPU installed, but the fans connected.
Most board fans will spin up and then beep or sown other other to indicate you forgot a fairly important piece.
The receiving Box being damage is never a good sign, but if a visual inspection does not show broken pieces on the board or in the box, the packaging is designed to take a lot of hammering.