Hey, anyway: PROBLEM SOLVED!!!! But a mistery remains...
FIRST (old) PSU: it was burned. I tried two cables: nothing.
SECOND PSU: defective (do you remember?)
THIRD PSU: once installed the PC worked... after some minutes: unable to power on... I uninstalled and reinstalled it: it worked!.... I turned it off, I unplugged the usb cable of the wifi antenna: the PC became unable to power on... I was thinking to USB motherboard connector issues...
It has been totally dead for several days... I tried to power on it every day, more times... NOTHING!!!
Some days ago, the turning point:
I thought: "let me try just another time...": I powered it on... and worked!!!
I was unable to understand...
So I went behind the PC and tried to plug the wifi antenna usb cable... I just touched lightly the case with the usb cable connector... and it powered off!!! Then I saw that when I touched it... I rested on the case with the other hand just a moment... and making this I touched lightly the POWER CABLE! And it turned off.....
CONCLUSION: the NEW power cable (of the 3rd PSU) was broken!
I installed a new one, and now it works normally!
Three strange "coincidences", three breakdown...
The internet connection was unable to work because in the same days the wifi router fell down and lost its wifi capab. We installed a new one (another brand)... but windows was unable to surf using it... and it got "blocked" when the windows PC was on... I installed a third router and all the computers came back able to surf...
Anyway, thank you for your help and advices!