I went through most of my collection of carbon mics tonight. The old ones are nearly always non-working when found: they pick up humidity, the carbon packs solid, and that's it; or the carbon granules dribble out over time.
Not all of them. I found several that still work, and a couple that I'd thought were dead (a Shure Brothers 3-A and a 3-B) aren't. Here are the working ones:
Here's my test set-up. The mic cable goes to a little mixer. It's isolated with 0.68 uF series condensers, looking at current across a 150 Ohm resistor in series with the mic, a 1.5 V battery and an added resistor to limit current -- I used 820 Ohms and it worked okay for checking. In practice, you trim microphone current for best fidelity with a carbon -- usually the lower, the better, but there's a point where it stops working.