When I connect my XBox 360 to my Dell All-in-One desktop through HDMI hook-up and switch to the HDMI source on my monitor, I get picture with no sound. How can I get sound?
The key-phrase is this:
Dell All-in-One desktop
This monitor is not even a monitor. It is a PC attached to a monitor.
The speakers may not be part of the monitor. It may be PC speakers that happen to be mounted to the side of the monitor, but hooked up to the PC.
You'll have to look at the specification of your device and see whether it really supports audio via HDMI.