When using a Gaming Headset with a PC and you have audio from the game but no microphone functionality it is likely that the game has a "Push To Talk" function initiated which means that a specific "Hot Key" needs to be pressed in order to allow the microphone to activate and allow the microphone audio into the game. This feature is used so that the user can control when the microphone is active and transmitting. Some games will allow the "Push To Talk" function to be deactivated and some will not.
NOTE: You can confirm that the microphone is functioning correctly by utilizing a basic recording program to record the microphone and play back the recording. If the microphone is detected and recorded by the recording program that indicates that the PC is detecting the microphone and hence the microphone is functioning correctly.