Screen shows message "no input signal" and monitor goes to sleep.

monitor show "no input singnal" error masage when not gating any type of video singnal ,
so if u realy check your monitor wires for correctty plugged in .
then:-

Two possibilities:

either the video/mainboard of the monitor is defective; or
the video card/ CPU is the faulty.

A way to verify is to try the PC with another monitor or to try the monitor in another PC.

thanks