You didn't mention PSU make and model. If you're not sure you can open the case side panel and read or take a photo of the sticker/label. Upload it somewhere like google drive or Dropbox etc. and post a link here.
Have you tried it without the extension cord? Plug the PSU directly to a wall outlet?
If you are referring to the suddenness of the issue, well, all components fail at one time. Sometimes it's total failure as the component won't work at all anymore and sometimes it happens gradually.
With better PSUs it's usually not sudden and total failure and even if they do fail they protect the other components that are connected to them.
update: i have 2 extension cord connected and i tryed the extension cord with no swtich i wouldn't even turn on, and i tried a wall outlet, and it still didn't want to ON. So the only thing that works is by using the second extension cord with the switch OFF for 5 sec and then i can turn it ON again and turn the pc on.
The root of the problem may actually be in the PSU, itself; however, if that has already been replaced, that is probably not the case.
If it works just fine at another residence, but doesn't at your residence, and you are using the same PSU to mains lead in both places; the issue likely isn't in the computer.
If you have plugged the computer directly into the mains connector on the wall at your residence, and the issue persists; you have a wiring issue that needs to be fixed, or there is a problem with the quality of power delivered to that outlet.
The difference is where it is being plugged-in, and you seem to have demonstrated that quite clearly.
If you have no Earthing at that outlet, it is possible that that lack is causing issues for you. Ignoring, for the moment, the fact that improper Earthing is horribly unsafe, I have seen the lack of Earthing cause some bizarre problems with a variety of equipment, over the years.
It merits your attention, if only to exclude the wiring as a possible cause.
something new has come to light. I was told to tried 1-by-1 to connect my mouse, internet cable, dp cable, headset, external fan and keyboard to see if it interrupts the start-up and i tried it. It seems that my DP-cable does the interruption.... when i disconnect only my monitor and the rest is plugged in it works fin powering off and on.. but when i connect it again i can turn it on 1 time only not restarting it when plugged in.. and tried all tre DP ports its was just the same.
Well, a bad cable could do it, I suppose, but I have never run into such a problem, myself.
Power issues are far more common, and it really could be a factor of the exact construction of the DP cable at issue, in conjunction with other issues that are hiding in plain sight.
However, if it is working now....what the heck. Run with it and see how things go.
You might want to take that suspect cable to your friend's house and test the theory that it is the cable in that setting. If you observe the same problem there, then cut that cable in half and bin it.