Computers have a power indicator that glows when it is receiving power.
On Desktops the front panel of the computer case has LED near the power button.
Try the following steps to resolve a desktop no-powering situation:
1. Try a different wall outlet, and power it on.
2. Reseat the power cord which is connected to the Power Supply of the system and power the Desktop on.
3. Swap the power cord of the Monitor with the system power cord and power on the Desktop.