Volume my computer volume is not working?

Did it stop working or has it ever worked before?

Make sure there is a cable running from your computer to the monitor's integrated speakers. It should go from a green 3.5mm output jack at the back of the computer to one the same size in the back of the monitor. If the cable is there and still no sound, double check the connection, make sure they are plugged in securely at both ends. Be sure that headphones are not plugged into the computer at the same time or audio will only come out through the headphones.

Make sure the audio is not muted. There is a mute in possibly 3 places. One spot is the application audio: if you're trying to play from Windows Media Player, make sure the audio is not muted near the slider and that the volume is loud enough to hear.
Second place is the system volume. In the Control Panel, Audio (Start menu, Settings, Control Panel, Audio component) you can check the volume and mute of the system volume.
Third location is the monitor speakers. There may be a way in the monitor's menu to adjust the volume for the speakers. Make sure it is high enough to be audible.

If all of those are unmuted and high, you might try replacing the audio cable. Also reboot the computer with the audio cable plugged in where it should be. (Sometimes high-def digital audio can be quirky). Next try plugging in a pair of headphones into the front of the computer and see if you're getting any sound through there.

Those steps should help you diagnose the problem. If not, just post back with what you found out through these steps.