Make sure there is power at the outlet, surge suppressor, power strip. Be sure any connected UPS is on. Try again.
Remove any recently installed hardware and go for boot. If the PC boots, check to make sure that the new hardware does not overload the old power supply - if it does, replace with a higher capacity power supply and go for boot.
Open the PC. Look for indication of power - LEDs, fan, etc. Replace the power cord between the outlet and computer if one is available, and go for boot.
If possible, obtain a power supply tester
to determine if the power supply has failed. Replace any failed Power Supply and go for boot.
Disconnect power. Disconnect all non-required cables and accessories. Leave only the power and data cables for power supply, boot drive, video card, mouse, memory and keyboard connected - everything else should be removed (with the exception of the small cables that go to the MoBo headers for LEDs, and switches on the case). Everything means both data and power cables. All controller cards should be removed as well unless using on-board or built-in controllers. Reconnect power and try for Boot.
Add devices, cables, etc one at a time to determine which is causing the fault. A PC that boots and shuts down shortly after could be an indication of overheating / over load. Clean dirt & dust from case, ventilation slots, etc. Make sure all fans spin freely - replace any that do not.
Those are some things to start working on.. hopefully, you'll find the problem and not have to go further. Good luck!