*That* may actually be the problem. The white plastic arm is driven by the pen-lift servo motor, and it should not start moving when the machine is first plugged in. The pen-lift servo motor is a component that wears out over time, and buzzing when the machine first turns on may indicate that it is not working correctly. When it fails, it can sometimes draw excessive current, producing a low-voltage warning.
I would recommend to follow along with the AxiDraw User Guide for the general steps towards making your first plot, including testing to see if the pen lifts up and down correctly, and if it can make a plot correctly. If it does not move in XY when you try to make a plot, then try disconnecting the servo cable, and see if that makes a difference.