Carbon mics need a bit more bias current. Most can be revived by physical shock, breaking up clumps of granules packed by gravity in storage/disuse.
Challenge: the carbon mic that got me into electronics and eventually Ham Radio, some 60-odd years ago!
Take a (sorta fist-size to shoe-box) cardboard box lid.
Take 2 razor blades (single-sided are best)with wires attached.
Poke those blades up through the box-lid beside each other, (just) not touching. A twist of the insulated wires might help steady them.
Take a section of pencil-lead and balance that across the blade edges.
Connect up - you've got a mic!