I have an older 2TB Barracuda that causes the power supply/pc to turn off instantly if plugged in. The computer will not turn on if its already plugged in. Would this simply be considered a short circuit on the HDD circuit board between pos+ and ground somewhere? If so, is it generally limited to the circuit board or could it be internal inside the drive as well?

More than likely the TVS diode on the PCB. Most times you can remove it or just lift one side and the drive will power up ok.
But best to test the diodes with a meter just to be on the safe side.