Standing Fan seizing up only when powered
I'm going to suggest that this fan has reached the end of its useful life.  It sounds like there is a bearing problem that is impeding the rotation.
This is almost certainly an induction motor and one characteristic of these is that once power is applied, the magnetic field from the stator not only tries to rotate the rotor but also pushes is axially forward or backward. So when you turn the fan ON, there is a force on the shaft that is not present when the power is off.  That's putting pressure on the bad bearing and stopping it from turning.