If the client is not producing any sound then the first thing to check is if sound has been enabled in the client. Under audio find the 'Audio Enabled' option in the 'Audio' tab of the game settings which are accessible in-game when Esc key is pressed.
If the client audio is enabled but no sound is heard, then it's possible that the EVE Online client has been muted in Windows Mixer. Check the volume mixer while EVE Online is running. Volume mixer can be opened by right clicking on the speaker icon located in the bottom right of the Windows taskbar.
If many programs are open scrolling to the right in the volume mixer may be required. Once located make sure that it is not muted and that the volume is set to a reasonable level.