The broken hinge is also next to the power button, so when the screen is opened, the detached hinge section pushes the plastic of the chassis upwards. This has both cracked the plastic, and made it impossible to press the power button normally.
I fixed it by using some really strong adhesive I found (called “plastic cement” or something like that). The power button is permanently wobbly, but you can at least press it now.
But exactly a week later the other hinge broke in exactly the same way. So more hours of my life and more adhesive later, it’s somewhat salvageable, but I am very gentle when opening and closing the lid.
Maybe I got unlucky with a shitty unit, or you got lucky with a non-shitty unit. Either way, I think our anecdotes cancel each other out.