You can FORCE a shutdown by pressing the power-on key and keeping it pressed down. In about 4-5 seconds, the Mac should just power-down.
You can FORCE a DVD to eject by holding down the mouse button as you power-on the Mac. KEEP THE MOUSE BUTTON PRESSED DOWN -- this should force-eject the DVD.
One other thought -- when your kid inserted the DVD, was there a DVD ALREADY INSIDE the drive? It could be jammed. This would probably require taking the thing apart to get at the jammed drive, to get it going again.