Was the hot end at printing temperature when you tried to drive the extruder stepper motor? Most if not all variations of printer firmware will prevent you from driving the extruder motor when the hot end is cold. If there is filament loaded in the hot end, preventing cold extrusions will keep your extruder drive from chewing into the filament or from doing mechanical damage to your extruder.

The small boards are the stepper motor drivers. There should be one for each stepper motor. On your x-axis issue, figure out which one of those boards is for the x axis motor and swap it with the board from another axis. This will help determine whether the stepper motor driver for the x-axis is bad.