Perhaps it would be best for the Arduino to be powered by + 5VSB and the start and stop button of the computer to be connected only to the Arduino. In this way, the Arduino (for example via an optocoupler) will control the start and stop of the computer. If this is possible, no additional power supply will be needed because the motors will only run when the main power supply is switched on at full power and the Arduino will be powered continuously from the + 5VSB line.