My Famicom's mic doesn't seem to work. I believe that any audio the mic recieves is being passed through to the TV, and when I try saying something in the mic, I don't hear the mic audio on the TV.
Might be worth just opening it up and cleaning it. Audio equipment is affected by dust big time. Isopropyl alcohol might do the trick. At the worst it probably just requires a little solder reflow to some cooled joints.
If you want to be sure it's not passing any sound through, you could hook the audio out up to your computer, open audacity, and see if the soundwaves change when you speak into the mic.
How do I clean the Fami's mic?
Clean the whole controller PCB and stuff with 90+% isopropyl alcohol and let it dry. Also scrub the metal part for the volume slider so it gets more shiny (don't use any metal polish or anything) with a rubber eraser or something and clean it too with alcohol. Be careful not to deform the metal part.