I had a SATA HD which, after 11.5 years of continuous service, failed to restart after a power failure. I could hear the motor spin, the head make a clicking sound, and then the motor spin down; this repeated for a few times before reporting an error. No luck changing the orientation of the drive, or gentle or less gentle shaking, or various folklore remedies such as a journey in the freezer.
Eventually I realized that the head is moved using a coil and a strong magnet, and so perhaps a bit of perturbation the magnetic field could influence the movement of the head in some magical way.
So I took a moderately strong magnet (the small tray in the picture, $1.50), and moved it around on the case of the drive. In some positions the head did not move, in some others it kept clicking, but somewhere in between I could hear the joyful noise of the head moving properly during the probe phase thus letting the drive spin up.
At that point, I could “dd” the content to a new drive and recover the system.