(When I was a sysadmin, I heard a story of how old VAX drives would stall, so holes had been drilled in them with tape over the holes. When stalled, the sysadmin would peel back the tape and use their finger to spin-start them. Those even older drives must have been more tolerant of dust!)
More than once I had a hard drive fail to start up after a power cycle (back then the drives only spun down when power was removed). First thing we tried was to remove the drive and give the whole drive a sharp spin on the axis of the platter. Due to inertia of the platter, this would tend to get the platter to move a bit and "unstick" it.
My recollection is that it worked every time I had to do this. Of course, we would back up that drive and replace it as soon as possible.
It still works on relatively modern drives. If the spindle or actuator arm is stuck, hitting the drive on its side (for instance by hitting a table with it) can free stuck movable parts. Worked well well into the 500GB era.
I went one step further: We had an old HP-UX machine with a failed hard drive that wouldn't spin up. The data on it wasn't supercritical but still nice to keep, so I was free to experiment. I removed the housing and pushed the platter by hand. It spun up, and while still open, I immediately took a full disk image with dd.
A more similar story to yours was with my 120MB hard disk on my PC when I was a, which inconsistently exhibited similar symptoms. I had no money, so always had to do with what I had (many stories sprang out of that). The hard disk was in a removable caddy, and when it refused spinning up, I simply took it out of the PC and gently bounced it on my bed right next to the desk. Put back into the PC, it then worked every time as I recall.
More than once I had a hard drive fail to start up after a power cycle (back then the drives only spun down when power was removed). First thing we tried was to remove the drive and give the whole drive a sharp spin on the axis of the platter. Due to inertia of the platter, this would tend to get the platter to move a bit and "unstick" it.
My recollection is that it worked every time I had to do this. Of course, we would back up that drive and replace it as soon as possible.