hard drive BLDC motor
The first thing I would to would be test commutation, you should be able to turn one pole on at a time and have the motor turn to that position (or just measure the voltage at the motor). An oscilloscope would be really handy to make sure your waveform is working right. 

You should see something like this:


Source: https://www.instructables.com/id/BLDC-Motor-Control-with-Arduino-salvaged-HD-motor/

Make sure there is no load on the motor (these motor's do not have very high torque loads)

You may need to ramp the motor's speed to get it to turn from a dead start.

Another thing you could try is run your code and then twist the motor by hand to see if you could get it to start.