Microphone not working on air

Check in this order:

1. Is the channel switched on, and the fader up?
2. Is the right source selected for that channel (mic, not line)?
3. Is a cough / mute key held or latched?
4. Is the cable firmly plugged in at both ends? Try another studio mic socket if there is one.
5. Condenser mics need phantom power (48V). Check it's on for that channel.
6. Look at the channel's meter: if it moves, the mic is working and the problem is routing; if not, it's the mic, cable or channel.

Swap to a spare mic to keep going, and report the faulty one so it can be labelled and repaired.