Hi.. I'm an experienced computer person for 36 years, have built my own computers, but have never seen what happened today.  I pushed the button to turn on my old, regularly used  XP machine, and nothing.  Pushed it again, nothing. Tried a third time. Nothing.  Figured I'd have to replace the power SUPPLY.  I turned on another PC (Windows 10) I have on the same desk (was connected to first computer by a KVM switch.. both have been working together for years) , and proceeded to do my email check, run Word and a few other programs.  About an hour and a half later I heard a "bing", looked over and the first computer had turned on by itself and was booting up.  It has worked perfectly since then and re-booted fine.  So, wasn't the power supply.  Faulty or loose switch?  Some sort of short circuit?  Have any of you ever seen ANYTHING like this?

This is my first post.  Appreciate any ideas.  To be safe, I've copied all my IMPORTANT files, photos, etc. and put on other computers and external USB drives.  I've always BAKED up daily all important files.
THANK you,
cuzzzzz.Me again... Did it again today.  pushed ON button, nothing after a half hour.  Left home, came back hours later and it was on.Whats happening is it's taking an inordinate time to boot proper...my 1st suspect would be a failimg HDD...DLoad and run the free diags from the manuf. site...run the long test.Is it "blacked out = Off" and then finally turns itself on with power light and booted?