If your client is not producing any sound output then the first thing to check is that sound has been enabled in the client. You can find the 'Audio Enabled' option in the 'Audio' tab of the game settings which are accessible in-game when you press the ESC key.
If the client audio is enabled but no sound is heard then it's possible that the EVE Online client has been muted in the Windows Mixer. To check you will need to have EVE Online running and then open up the 'Volume Mixer'. This can be opened by right clicking on the speaker icon located in the bottom right of the Windows taskbar.
You may need to scroll to the right in the mixer until the EVE Online client is located. Once it is please check that it is not muted and that the volume is set to a reasonable level.