So I have found why there was the problem with no signal when I booted my PC.
How I wrote I switched the switch on the card and after that it worked. The switch was there for switching between BIOS and UEFI mode. I really do not know what I had there for the first time switched, and I do not know on what mode I am running now. But the mode what was switched from the factory did not work for me. I did not know that I should switch it, because in the manual is not anything about it.
What I have read my motherboard supports the UEFI mode, but I do not know if I should try it, maybe later. What I have heard the UEFI mode does not improve performance, and it's a bit complicated, so I'm not in a hurry. And I do not know how to set it... so I have to study the process.
But after this I ran into another problem. I wrote here that I had problem with some actions in the Windows what lead to the black screen lock and I had to restart my computer many times. So I tried some things, mainly with drivers, and now it works with no problem and I hope it will stay that way. I test it for 3 days and it works fine.
And I have to say that the performance is just great. In performance it is what I wanted. Just it is a pity that the first impression was not very good. Just hope there will be no more problems.
Anyway thank you for your all help.