There is another way which works for me.

If the actual hinge still works and you cannot get another, consider drilling through the hinge into the case. If possible, try to find two places diagonally across the detached portion of the hinge. Drill the two holes and use two stainless steel 1/8 bolts and nuts to fasten the case to the hinge.

Here is the important part. Start the bolts from inside the case using a couple of fender washers (washers with a wider shirt than normal washers) to bind up more of the case than just the screw head or screw head and washer. If the fender washers overlap each-other, use a pair of tin snips to flatten the mutual sides so that they appear to be two "Ds" facing each-other. Run the bolts out through the holes in the hinge and use the nuts to snug down. You may want to use additional washers on the outside, if the hinge metal is weak, but if not, then the rest is relatively straight forward.

Mark the protruding end of the bolt and either cut it off with a Dremel tool (small hand held drill) or just before you snug up the nut, dab the threads with super glue, snug down the bolt, and then use a grinding bit on the end of a drill to grind the bolt down to the surface of the nut. (Stop periodically to ensure the bolt is not overheating the case).

You are left with a solid working hinge and the smooth bolt head on the inside, where it can be covered with a felt dot, to prevent damage to your instrument.

Incidently I have used a similar technique to put an eye bolt at the top and bottom portions of my cases, to attach web slings to. This allows me to sling my longneck banjo over my shoulder like a rifle or both the banjo and guitar for long carries. With a double eye snaffle hook at each eyebolt you can use your instrument strap as a case strap. Good Luck!