As a tech, I've seen this issue several times and every time I've seen it, it was a different piece of hardware causing the issue...
The first thing I try is connecting a different power supply that has a similar watt output. That means completely disconnecting your current power supply and connecting everything that had power before to the different power supply. I have found that the power supply is the most common failure because the power to our homes isn't always as clean as we think it is and too many brown-outs or power surges, no matter how minor, can take a toll on a PSU even with a surge surpressor.
The second thing to try if the power supply doesn't make a difference is to disconnect any PCI/PCIe or Graphics cards, disconnect any extra drives (leave primary system drive connected), and remove all of the memory; then try turning the comptuer on, if it is working correctly, it should buzz/beep at you because there's no RAM. If you get no buzz/beep, the mobo could very well be shot. if you do get a buzz/beep, try putting in 1 RAM card at a time and try turning on the computer. if it works, keep adding hardware back to the computer until you find the culprit. Once found omit it or replace it!