PC problem

This sounds silly, but when you changed the monitor did you also change the monitor cable? I went through a similar troubleshooting process a few years ago and the faulty monitor cable was literally the last thing I checked.

When mysterious things happen with a computer I find that most of the time it's a PSU issue.

Also when trouble shooting it's kind of important to know if the machine turns on at all, and if it beeps and all the fans spin up and so on.

Do you have your old PC or could you borrow a friend's to troubleshoot ?
Swap everything swapable [GPU, Memory] and see if they work.
Then swap their PSU into yours and test that. Do NOT test your PSU on another PC, if its the point of failure, it could affect their hardware.

If its not GPU/Memory/PSU, it will most likely be a motherboard issue.

Edit: When swapping, go one by one. Don't swap GPU and memory at once, not even all memory sticks at once.

It's too hard to diagnose with any accuracy without sitting in front of it (and being able to swap out parts).
If I had to hazard an educated guess - like the others, I'd say it's a PSU or mobo issue at this point.

You can test the PSU with a multimeter (google how to) and if you have another available, swap yours out and see if it solves the issue.
Also, try resetting your BIOS (you can google how to do that as well - usually just take the CMOS battery out for a couple minutes).

what i'd check:

• if a mainboard speaker is installed and you get a single regular beep sound at boot it doesn't recognize anything as broken
• the diagnostic led on your mb (bottom left if one does light up red it tells you for what to check) *cpu, dram, vga, boot-hdd
• unplug monitor from power switch it on and off once + try another cable and if possible other plug; > dvi-hdmi, dport-hdmi ...

could be anything, but if the board speakers are on, and you get no beep (error beeps were enabled in bios) and your diagnostic
leds don't light up red or something, (while the computer itself runs * "fans and stuff") with no other error indications
chances are very high the video card is faulty - being able to pop that in into another system would let you know for certain

Sounds pretty weird. Given that it's two different cards, which I assume were working to this point, I suspect the power, either from the MB or the power cables. Do you have any GPU that doesn't require extra power, i.e., takes power only from the slot?

I ordered a new mobo, same model.
Same problem.
I've done all troubleshooting again before, nothing worked.
I was saying a long series of "porcodio" and "porcamadonna" when after a minute or so, pc booted with an old GPU plugged in.
So the probelm was the GPU and my fault was not to be patient, because apparently, when you put a new hardware on this mobo, it has to be a 30-40 seconds cycle of led blinking and so on..
Thanks for your help and your suggestions.
Now I've to buy a new GPU..
Based on my config, wich one you will suggest? :D
I'm oriented on asus strix gtx 1060 6Gb. There is something better price/quality?
Sorry for my english XD