Actually, these TV sets have a flawed design that under the right conditions inverts magnetically. Since they are plugged in when this happens, it causes the usual polarity of the wires running through the walls --which, like everything else, is normally aligned with the fundamental electro-harmonic resonance of the Earth's magnetic field, and therefore causes no problems-- to reverse itself. As soon as this polarity reversal occurs, the wires in the walls REPEL the nails, pushing them out of the walls at high speed, like bullets. This requires less energy than pulling them out would, since you are just reversing the direction that the nails were put in, using a reversed polarity. Since the wires are connected to the city's electrical grid, they have plenty of power available to do this; it is not dependent on what is inside of the TV; all that does is initiate the reversal. Then the power of the city's electrical grid provides the rest of the energy needed. Sometimes when this event occurs, the neighbors' electricity supply "stutters" a little. Ever had your lights flicker or your TV set stutter a bit? It was probably due to this happening somewhere nearby in your city. So you see, the nails don't get sucked into the TV, they get pushed out of the walls.
Once any one of them touches the TV, though, it discharges the imbalance and stops the process, much the way a spark from your hand to a doorknob discharges a static buildup. The kid was just unlucky enough to be in the path of one, before the first one hit the television.
At the risk of oversimplifying, perhaps the easiest way to explain this comes out of the movie "Young Frankenstein":
You connect the plus to minus, and minus to plus...
I think I have seen to many 1950s sci-fi flicks...