Yes, it's the tried and true 'turn it off and on again' process, but it works. Reboot the PC and connect the headset once again to let Windows reinstall them. Head to Device Manager and uninstall the drivers for the connected headset. If your headset isn't working, the problem might be in the drivers. Should you have software like Realtek's HD Audio Manager, try disabling jack detection and see if that helps.
Newer motherboards come with numerous ports for surround sound, so you might need to hit up the manual for more details. Mix those two up, and nothing at all will happen. Is it plugged in? Have you utilized the correct port? For 3.5mm jacks, it's generally green for output and pink for input, depending on the available sound card.
Corsair HS50 Pro fixed cable (Image credit: Ben Wilson | Windows Central)