My brother-in-law works at the Argonne Labs, so he's a pretty smart guy. He sent me this:
Although I did not try the experiment, I am sure that the candle "demonstration" is a hoax--it is physically impossible. There are several physical principles that are violated here. First, the circuit is not complete--the candles appear to be physically separated. For electricity to flow there must be a complete circuit that includes a source of electric potential such as a battery, a generator, a photovoltaic cell, etc. Second, the candles themselves are made of wax--an electrical insulator. No electricity can flow through wax--at least not enough to light a bulb or make a motor turn. Third, the magnetization of the nails is a red herring. Magnetic fields can be used to generate electric potential only when moved with respect to a coil of wire. In this demonstration, there is no coil and nothing moves. This is either a magician's trick or done with some clever video editing.
Later he sent me this:
I looked again at the candle-power video. I'm convinced that this "works" by way of a trick. For example, if the demonstrator (a magician by trade, no doubt) hollowed one of his candles to hold a battery and modified the "nail" that went into the candle so that it had two small wires running along its length and modified the alligator clip lead to have two wires running along it (each attached to a separate, electrically isolated alligator "jaw"), he could form a complete circuit and run the lamp and the motor from the battery. The other candle would then just be a dummy prop. Also, watch the video and note that when he blows out the candle, his left hand slips under the table out of view, perhaps to activate a switch of some kind. In any case, there is no way that this can work as advertised.