Here’s my theory.
The lift with no ram or safety bar is designed to stop relatively close to what we see in the pics, there was some rust in the pivots but the hydraulic rams were plenty strong enough to overcome any resistance caused by the rust.
The lift was lifted without the weight of a vehicle on it, the manual says it takes about 300lbs to lower the lift, but with the rust in the pivots, it would have been more than 300lbs.
Now add the fact that it was forced even further past it’s designed range with a bottle jack and the rust in the pivots, and you got yourself a stuck lift.
Wrap a chain around it and a bottle jack, and I bet it goes down.
People have suggested putting a car on it, I think that would work too, but the only way I would do that is if all the hydraulics and safety bars were reinstalled, then the car was jacked up high enough to slide both lifts in place and slowly lower the car onto the lift, then lower it as normal.