The problem needs to be narrowed down to the computer, to the sound card, to the configuration, or to the headset.
Do other headphones work?
What about the sound card you plugged into - is it the selected Playback Device? Remember to check Properties via any other Tabs that may be available. Very easy to forget or overlook some relevant configuration setting.
Try the headset in a non-computer headset port: tv, radio, ipad. Can you hear the sound, the stereo effects, etc...? Likewise for the microphone if you have some other device accepting microphone input that you can test and hear.
Can you hear any clicks or static when the inline control is moved?
Can you hear anything if you gently wiggle the plugs, then along the length of the wires, both ends in and out of inline control, and all the way up to the headset? (Trying to see if a break can be detected.)
Eliminate or reduce the possibilities. Only change one thing at a time.