the system power comes up, does the monitor power come on? Most monitors have a status LED on the front bezel that should show green, orange, or blinking if the monitor is powered on. You can hear CRT monitors power on with a gentle sound, though I can't describe it beyond saying it's the sound of a CRT tube warming up. Make sure the monitor is plugged into a good outlet by testing the outlet with a lamp or any other device that will prove beyond a doubt that the outlet is good. Make sure that the power cord is either permanently attached at the monitor end or that it is seated fully in the socket, since partial cord insertion is the most common failure for monitors with detachable cords.
LCD displays don't make any sound when you turn them on, but they don't have a simple power cord, either. Older LCD monitors are usually powered by an external transformer, which in turn is powered from a regular AC outlet. If the LCD display doesn't show any signs of life, make sure that the cords into and out of the transformer are fully seated. Some transformers are equipped with a status LED to show when they are operating. The power connection to the LCD display is often awkward to inspect, recessed into the back of the display. The important thing is to make sure it is started correctly, then seated all the way.
No Sound From all speakers
Check that the speakers are powered on.
Check that the speakers are connected to the correct ports on the PC. This is particularly important If the customer has both integrated sound and a sound card.
If the speakers have a volume control button - ensure that this is turned up.
Check that the Windows Audio service is running. If this is not running then many of the subsequent troubleshooting steps will not work. Go to Start->Run and type services.msc. Double cliick on Windows Audio. Select Start if possible and check that the Startup Type is Automatic. Click OK.
If the speakers are digital speakers then try forcing the sound card to use digital. Go to Start->Control Panel->Sound and Audio Devices.. On the Volume tab, click the Advanced button in the Device Volume section. In the Volume Control window, below the Play Control Volume slider, click Advanced. If this does not show select Advanced Controls from the Options menu. Select Digital Output Only
If possible try an external audio source like a Walkman, CD, or MP3 player (connect the speakers to the headphone jack)
Check that the volume control in Windows isn't muted or turned too low. See the screen shots below. Go to Start->Control Panel and double click on Sounds and Audio Devices.