Brand new iMac won't power on

I have just unpacked a brand new iMac 24-inch, model A2438, and it simply won't power on. The cables are put in correctly, the plug is in the socket and on. The screen remains blank and black. There is no chime, nothing.

I have tried pressing the power button for different periods of time, using different plugs, unplugging the machine for different periods of time, and so on, and it simply does not respond.

There appears to be no damage to the machine.

This is not my first iMac so I am very confused. Is this a known issue with this model?