Make and model monitor, connection type? Age, condition?
Is the monitor on (showing signs of having power) via LED's, power light, etc.?
Be sure that the monitor is plugged into a working wall outlet. (Check for tripped breaker or blown fuses.)
Have you tried other known working video cables? Other power cables.
It the monitor connected to a GPU? If so. remove the GPU and try the motherboards built in video connection.