The Arduino library you are using is intended for use with H-bridges or darlington arrays, not with the simpler A4988 interface, so it is not producing the proper step/direction inputs for your driver. If you want to test out the driver, your Arduino code can be quite simple: set the direction pin high or low and toggle the step pin; every low-to-high transition on the step pin will step the motor once.
You might find this thread (and its sample code) helpful:
