The phrase "to turn on" means to activate or make the state of something different than it was before in such a way that it did not have a certain property before the action, but once turned on it does. IT can also mean that a certain property is made to be no longer dormant.
For a light being turned on, this means that the property of light coming out of the light and the electrical current now flowing through the light is present but was not before. Before a light is "turned on" it doesn't emit light, but afterwards it does. For a chainsaw, the property of movement in the chain doesn't exist, but after it is "turned on" this property does.
The same thing goes for the serial killer's "switch [that] went on". This means that his desire to kill was "turned on" or activated at that moment. He realized his desire to be a serial killer. His "property" of desire for killer was nonexistent, or dormant, before he was "turned on," but after he was, it became active.
The video and TV, on the other hand, have already been turned on so it is not be referring to them.