If when i retun computer from "display off" by moving cursor, my signal returns to dim or black (SOMETIMES), yes there is a signal, but there is a dim-black, or black signal, sometimes turning off and on monitor by button will result in blinking right picture and again goes off on black or dim-black, in other scenario turning monitor off and on will result in getting good picture back.

1. If a graphic card is faulty, does turning monitor ON and OFF has any effect on graphic card to fix its sending signal?

Other thing is that I connected same monitor on laptop via HDMI again, and not single time it did make this problem, on same resolution, and on same Hz as desktop PC.

2. If a monitor is faulty, why did I not get any single problem while being connected to laptops HDMI?

Those two questions are important, mostly first one about does really graphic card as a hardware can be affected with turning monitor on and off.
Please do not come with drivers solutions and similar things, rather answer my questions, as I'm a geek for software I know when something is wrong with hardware, and I need stronger geek for hardware on this, who will understand what I ask and why I ask.

Thanks in advance.