Although it uses a standard audio plug and thus the built-in sound circuit of the motherboard, double check the output device. Your video card may have hijacked the audio through HDMI.
Also, assuming you're having a Realtek audio circuit, check the Realtek control panel to have the jack assigned to Speakers/Headphones.
And yet another thing: Does your computer have separate jacks for speakers (often green) and microphone (pink)? If so, does your headset have only one plug? If that's the case you'd need a splitter. A normal stereo plug is divided into three but if there's four sections (tip-ring-ring-stem) one is for the microphone. The microphone jack is also stereo but computer microphones are usually wired to split the signal for both ears.
