So according to Sherlock Holmes "When you eliminate everything else, whatever is left, no matter how improbable, must be the truth"
So I went with demonic possession. It fits the facts because something was making the green light on the speakers go on. Did I mention I've watched too many episodes of Buffy and Angel?
So the reason the speakers don't work is that we didn't know exorcism well enough to fix the speakers.
Sherlock Holmes was an intuitive reasoner, which meant he was a good guesser. Since he had a good writer, wouldn't you know that Sherlock was almost always right?
The morale is that you can have a theory that fits all the facts and still be wrong. However the explanation makes us feel better because it means we were brilliant, but it was beyond our ability. Now if I could only think of a magic spell that made me truly believe it. That would be something.