analogRead returning 0 constantly when connected to joystick
Follow these steps to identify the problem.


Disconnect A0/A1 from Arduino and use a multimeter to check the voltage coming from the joystick X and Y. If it swings from 0 to 5V....the problem is in the Arduino. Check your code and connections. Maybe your wires are damaged?
If the voltage is not changing at X and Y pins, disconnect power from the joystick and use a multimeter to check the joystick potentiometer. Check all three terminals in each axis of the joystick. If R is the measured resistance between the two outer pins, then the resistance between the central pin and each of the outer pins should vary from 0 to R depending on the position of the joystick.
If there is no problem at all with the joystick readings by potentiometer then the problem has to be on the Arduino side.