On a boards' parallel connector try to find pin which in board manual is DIRX and DIRY. When you change axis direction, state of this pin should change from low to high TTL logic signal or opposite (depends upon settings in Mach3). In your case it should happen for sure in case of Y and Z axis. For some reason X axis doesn't receive direction signal from pin DIRX but only STEPX, causing it to rotate in one direction only regardless pressing left or right on a keyboard. When you find on your board connectors pins DIRX,Y,Z try to make connection(bridge) from DIRY or DIRZ to DIRX (disconecting cable from computer and power off). If after bypassing DIR signal X axis works in both direction that's mean fault is in a cable or computer parallel port. You can check signal outputs on an end of the cable. Step signals are pulses so it will be visible on oscilloscope rather than voltmeter. Direction signals are changeing only when you change direction so it should change from 0V to 5V or opposite so you can use voltmeter. But always be careful when messing with computer's parallel port it's not protected hence easy to damage by static electricity or shorting it to the ground.