In desperation I’d first try (if you haven’t already) all the different usb ports in case it’s a faulty port. Then a different USB cable, assuming it’s not built into the case. If it has some external power supply I’d try a different one if possible.
Beyond that, by “very old” do you mean spinning rust, or are they SSD?
Either way, there’s always a way to get into the case, if it’s a popular enough drive/case, there may be a video on how to do it. Depending on they type of drive there maybe more you can check on the inside.