As you can see in the attached pic, the return value of AnalogRead(0) is pulsating from some value to zero. Sample time is 50ms.
I am using Arduino Due with MegaMoto*) shield. A0 input is supposed to read current sensing from MegaMoto. I tried to measure A0 to GND with multimeter but no pulse is detected. I have an external sensor connected to A1 and was read fine with AnalogRead(1).
Connect a potentiometer to A0 and check that you can read the input.
Do you use a breadboard with bad connections ? The graph of the measurements is typical for an open input or a missing ground.