Few different things it could be:

• Battery is flat.

  Lithium ion batteries should come with a small amount of initial charge but this is not always the case; try charging the battery for a few hours first.

  It's also possible that the battery may be faulty, or may have been left without a charge on the shelf for too long which may have damaged it.

• Camera is on, it just doesn't "look" on.

  A DSLR in photo taking mode will typically not show anything on its LCD screen, you have to look through the optical viewfinder, and the controls in the optical viewfinder may not light up or do anything until you half-press the shutter. Press the shutter button or the play button and see what happens.

If you have charged the battery for a few hours, and tried pressing the shutter, etc while on, and still no joy, simply take it back to the store (or to any camera store). It should be easy for the store employees to tell if there's something wrong with the camera or battery and if so, hopefully you can get it swapped for a working one.