Power cables sometimes wiggle loose from monitors over time or after being moved around. Checking every point where electricity is delivered to the monitor is usually an early troubleshooting step when a monitor is blank.
The power cable connected to the monitor should fit firmly in the three-pronged port on the back of the monitor. This power cable is usually of the exact same type as the power cable to the computer case but may be a different color.
Warning: Make sure you power off the monitor, using the power button on the front of the monitor, before securing the power cable into the back of the monitor. If the monitor is powered on and the other end of the power cable is plugged into a working outlet, you run the risk of electric shock. Trust me, I've done it. It hurts.
Note: Some older styles of monitors have power cables that are "hard wired" directly to the monitor. These cables do not typically come loose. If you suspect an issue with this type of power connection, keep your personal safety in mind and do not service the monitor yourself.
Replace the monitor or seek help from a computer repair service.