I assume that you are using this configuration.
It could be that connecting springs in the Microphone socket of the PC have lost tension and therefore are not making good contact with the plug.
It could also be that the wiring in the microphone plug itself is loose.
Try the following: While speaking to someone over the microphone, firmly hold the microphone plug when it is in the socket and gently flex the cable at the rear of the microphone plug. If the 'voice' is lost it may be that a wire is loose in the plug. (or that you are not holding it in firmly enough). If the 'voice' is not lost it probably is the socket that is faulty.
As it is a new headset, I'm assuming that the microphone plug itself, which is connected to the headset cable is OK as over time these can wear, by being inserted and removed often over a period of time, and cause a similar problem.
Not knowing what type of PC you have means that I can only give a general answer as how to fix the problem.
A lot of PC's/laptops have the microphone socket mounted on the motherboard and therefore it is difficult to repair them. If you are fortunate, especially if you have a PC, and the microphone socket is connected to the motherboard via a cable connection then you may be able to buy a complete 'panel' with microphone/headphone/USB socket which you can install in the case and just transfer the connections. In the case of laptops sometimes the mic/headphone sockets are also connected to the motherboard via cable and the socket 'board' is actually a replaceable part.
Hopefully this is of some help