Power problems can manifest themselves in many different ways and the problem that you are having could be power related yet nothing to do with the AC adapter or main power brick, a break in the soldered circuit or a system short as two examples of what could interfere with the power supply to hardware such as the HDD/HDD port on the MB.
Other thing I am going to try is she has another Toshiba that uses the same battery. If this battery powers that PC, then I would definitely say its the mobo or something on the mobo.
That would be a good test but only if both batteries are the exact same or have the same voltage and the battery from the problem notebook has a higher amperage than the known working notebook battery has.
FWIW: A bad CPU could also result in a black screen but would not stop power getting to the HDD etc and that is why I have not suggested a bad CPU as the possible cause here.