No conspiracy theory ever dies or even fades away. It just waits around to be revived again and again. There is no credible evidence of any power cut at the TSBD. Nor is there is any reasonable explanation for why any conspirator would cut the power or phones for a few seconds. If the purpose was to keep the police from using the elevator, that would also preclude any assassin from using it to escape the building. Instead it places both the police and assassin on the stairs. And how exactly would such an event be coordinated? It is preposterous. No reason to reiterate all the prior discussions but it's clear that Hine is referring to the fact that there were no incoming calls at the time the motorcade approached which allowed her to go to the window to take a look. Her use of the phrase "the lights all went dead" is used in conjunction with the phone which was her responsibility to answer. She is simply saying there were no incoming calls at that moment which allowed her an opportunity to take a peak at the motorcade. Photos also confirm the Hertz sign atop the building was functional at 12:30 moments after the assassination. So there was power on in the building.
Mr. BALL. Did you stay at your desk?
Miss HINE. Yes, sir: I was alone until the lights all went out and the phones became dead because the motorcade was coming near us and no one was calling so I got up and thought I could see it from the east window in our office.
Later in her testimony Hine said that right after hearing the shots - which she said sounded like they came from within the building - she left her office and tried to contact people working in the other offices. She knocked on one office but the person inside was on the phone and couldn't hear her.
Miss HINE. And there was a girl in there talking on the telephone and I could hear her but she didn't answer the door.
Mr. BALL. Was the door locked?
Miss HINE. Yes, sir.
Mr. BALL. That was which company?
Miss HINE. Southwestern Publishing Co.
Mr. BALL. Did you call to her?
Miss HINE. I called and called and shook the door and she didn't answer me because she was talking on the telephone; I could hear her. They have a little curtain up and I could see her form through the curtains. I could see her talking and I knew that's what she was doing and then I turned and went through the back hall and came through the back door.
It seems to me that she was simply saying that no calls were being made - either in or out by customers or workers - at the time the motorcade approached not that the power was off. That's why the lights of calls on her phone went dark. So she took that opportunity to go watch the motorcade. But people - or more accurately one person - in the other offices was still using the phone.
Her full testimony is here:
http://mcadams.posc.mu.edu/russ/testimony/hine.htm