To me....it sounds like you have a dead or shorted piece of hardware issue causing the failure to even start... I would first disconnect the 24 pin power connector to the motherboard and Reseat it firmly and check all hardware power and data connections and reseat ALL.
If no luck then disconnect ALL hardware...ie cd/dvds, remove one of two sticks of ram, mouse, graphics, and anything else including the hdd power...then try to power up and watch for fans spinning etc..to see if a piece of your hardware has failed or shorted out...you can quickly narrow down to PSU or HARDWARE.
The above steps are for determining of you have a bad psu or a bad peripheal...if you get the machine to start...begin reconnecting one piece of hardware at a time by shutting down and reconnecting one piece of hardware and attempting to boot...if good...shutdown again and connect another piece...once power on fails...you will know or alternatively.... if all hardware is disconnected and it still fails to start...you have either a bad psu...a bad motherboard...or a dead cpu.
There are ways to check the psu by itself...mainly by shorting a green signal wire in the 24 pin motherboard connector to a black gnd wire pin but unless you know what you are doing and am comfortable with electronics...I wouldn't do that as you can blow the psu if you don't know what you are doing..there are pictures and videos of how to do this online so you can go and look for yourself to decide.
IF YOU GO THE ROUTE OF SHORTING THE SIGNAL WIRE TO GROUND...UNCONNECT THE POWER SUPPLY TO EVERYTHING PERIOD...CONNECT NOTHING OR MAKE SURE NOTHING IS CONNECTED TO THE POWER SUPPLY.
If you aren't comfortable with shorting two wires together to get the psu to start without being connected to a motherboard...then you need to get it tested...if you have another machine....you can plug it into it to see if it works...if not take the power supply to a repair shop to have the psu tested for output.
You have to determine if the psu is providing voltage or if it's dead...once you do that you can determine your next steps if it works and if not...you have your answer...if it works..then follow the reconnecting one piece of hardware at a time and attempt to start...if power works...connect the next piece of hardware...if it fails disconnect the last piece connected and see if the psu powers up...if no...you have the offending piece of hardware and so on...one thing to eliminate the motherboard itself...reconnect the 24 pin ONLY and attempt to power on....make sure nothing is connected to the motherboard..ie keyboard, mouse, jump drives..usb connections, graphics...etc...we're not checking for POST...Power On Self Test....we're just checking to see if we can power up the PSU.
Hope this helps you narrow down what is going on with the power or psu itself.
Respectfully,
tekman42