Check your monitor's manual how to set it up via the buttons you usually find on the right hand side of the screen. Might be set-up wrongly so try auto set-up. It will 'sleep' if PC is shut-down.
It could be your graphics card has failed, so look at the back of the PC to see if you have more than one connection for the monitor, if so, try the other one and boot up.
If the monitor shows 'going to sleep' then that makes me think the unit is OK as it shows some graphics.