J Miller

Caroline,

That case is mostly masonite. The bottom, ends and sides are any way, and I'll bet most of the top is.
On cases like that I take them completely apart, remove the staples and clean the areas I'll be gluing.
Then I use the larger clamps to hold it together as I put new nails into the holes the staples left. It's much less damaging to the narrow edges of the end wood if you can use the original holes. The barbed paneling nails work wonders here.

Once you get it glued and nailed, clamp it, clamp it, clamp it. That's about all you need to do on that one.

The top is gonna be a big pain. As broke as it is, you might as well just take it all the way apart and start over.
I've had to do that with a couple and it's really better than just fixing the separated areas.
On the inside use a sharp blade to cut the inner covering where it's not already torn. That way you can glue it back down when the wood is fixed.
On the outside you can carefully peal the covering away from the wood, then fix the broken wood and reglue the covering.

Joe