My daughter's Toshiba laptop is having problems turning on.
We checked the voltage of the power supply and it is 34 plus volts; supposed to be 19.5 volts......
We don't know how long it has been this way.... and we don't know if the power 'fluctuations' are regulated by the battery or internally.
The battery is supposed to be 10.5 volts; we can't tell what the voltage is now because the multiple connector pins are covered on the battery.
The 'turning on' problem happens with or without the power supply plugged in.

Did the excess power supply damage the battery? or the computer or both?

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