Step 1: Remove Bezel
In the first photo you can see the broken hinge, normally that metal plate is captive between an inner plastic frame and the bezel. There is a lot of torque on the hinge when opening it and when the screw failed it resulted in the bezel breaking.
Step 2: Hammer Time!
Next insert the tacks from the back of the screen through the holes you just made. It is a tight fit, so use a nut driver or socket as a hollow punch to drive the hinge down over the tack.
Once the tack is flush with the back of the screen, use a punch to fold the tip over or peen it to lock everything in place.
Step 3: Revel in the Renewed Hinge!
I think the fix came out nicely. Adds a bit of contrast to the back of the machine if you're into that sort of thing, and works just fine regardless of aesthetics.