First thing to try is changing electrolytic capacitors. To get to the caps, the drive's disk tray needs to be dismantled. It took me a while to figure it out, but its done like this:
Mounting bracket and casing of drive has been removed (easy). If you need to use force, you are doing it wrong.

Step 1.
Remove lock-screw and spring, marked in the first image.
Push the disk ejection button to release the upper disk holder mechanism. Push it forwards-downwards to release it.

Step 2.
Remove springs marked in second image.
Push disk eject mechanism forward to release it.

Step 3.
Replace the five caps, marked C08, C09, C10, C11 and C05. I used EMLF160ADA100MD73G as replacement caps.
After this the drive works as expected again.