Two things to check on.
1. The CONNECTOR on the cable from the headset. On almost all common PC systems the connections for EARPHONES and MICROPHONE are separate 3.5mm sockets on the case - usually the front, but sometimes on the back, too. So the cable from a combo headset needs to end in TWO separate 3.5mm male plugs to go into those sockets. EACH of these will have THREE contacts: Tip, Ring and Sleeve, abbreviated TRS. Sleeve is Ground, and Tip and Ring are the two stereo audio lines, whether earphones (output from the audio chip) or mic (inputs). For the MIC connection, it is designed to accept 2-channel stereo mic input, although most headsets actually have only a mono mic and feed that signal on ONE of the input lines.
However, there is another connector design commonly used on Apple equipment and on many high-end systems. This type has only ONE connector on the end of its headset cable, and it has FOUR contacts: Tip, Ring1, Ring2, and Sleeve. Abbreviation TRRS. Tip and one Ring are stereo left and right OUTPUTS to earphones, and other Ring is mono INPUT from the mic. (even among those three, there are some variations of which is which!) Anyway, if you have that connector and plug it into either of the front sockets, it does not work. But you can get an ADAPTER that accepts that 4-contact jack and converts it two TWO 3-contact jacks, one each for earphones and mic, that you plug into the two jacks on a PC.
2. Setting Input device. Any computer MAY have two or more sound devices. For example, there may be an audio chip on the mobo (VERY often by Realtek), another audio output chip on the video card so sound can be sent to a monitor with speakers via the HDMI cable, and a third-party sound card in a PCIe slot. But Windows can use only ONE audio device at a time. Within Windows where you can configure your sound devices you get to specify exactly which device will be used by default for EACH of three functions: sound OUTPUT (e.g, speakers and / or headphones), sound INPUT for a mic, and MIDI output devices. These three items are set separately. In the search box at bottom left of the screen, type in Control Panel and use the menu to get to Hardware and Sound. Under Sound choose Manage Audio Devices. On the Playback tab you can select the default output device, configure its details and test it. On the Recording tab you can specify the input device, configure that and test. Note here two things. Choosing the correct PLAYBACK device does NOT also select the default RECORDING device - they are set separately. And in the RECORDING device panel, the front mic jack, any front Line In jack, and the rear panel Line In jack all are different inputs, so you must choose the one you are really using.
So for example, your relative's system may be set to use the mobo Realtek audio system as the default playback device so that sound comes out of the front earphone socket and the mobo rear panel Line Out socket. But it may NOT have been set to use that Realtek system to receive INPUT from the front panel mic socket.