It is completely possible that the port you are trying to use it in is output only rather than output/input which is what you would need for a mic/headset combo.
Before doing anything, test the headset in another device that you know for sure works as both input and output. Say a smartphone? If the headset and mic work there, then you know it isn't the problem. However, if it doesn't work right in the phone either, the headset may be the problem and you would need to return/exchange it.
Now if the laptops port is actually output only, then you have three options...
1. Purchase an adapter that will take the 3.5mm input/output plug from the headset/mic combo and turn it into a USB connection.
2. Return the headset/mic combo and get one that comes with a USB connection already (no 3.5mm).
3. Keep using it without the mic working, so you would only get sound through the laptops internal mic.
Note: If the port says it is supposed to be both input & output, then I would check on if the laptop is still under warranty. If it is, get them to repair it for you. If it isn't, then you would need someone to replace the port.