Successfully replaced the hinge on my computer (the one I broke back in my last comment.) The failure point for me here was all four screws (the screw heads sheared off) that attach the hinges to the display assembly on both sides of the display - that is, the screws that screw into the 2-screw piece on the hinge.
If anyone has the same issue (screw failure) here are the screws I bought to replace them:
M2.5 x 4 mm Nickel Torx Head Machine Screw #10296, on MetricScrews.us