I would first test your computer and see if there is sound without using the headset. Do you have speakers or a cabled headset?
Some games have an option to chose which device you want the sound to go to. For instance in WoW you can set your headset as the primary and you will only hear from that. If you have your speakers set as the primary you will hear them from that. If you don't have speakers, you won't hear anything.