Here is some great tips from Call That Girl for trying troubleshooting why your computer will not turn on. Sometimes it's the littlest thing you take for granted that is making your computer from power up.
When in doubt you can always Call That Girl for more help.
Tips:
Go to the back of your PC tower and check all the cables.
Jiggle cables and make sure things are secure, or to be certain…unplug them all and plug them back in.
Check that the power from the wall outlet is working if the PC isn’t giving you any power at all. If you need to, plug it into another outlet or reset the surger.
Check the power cable to make sure it has not been unplugged (especially in office settings, cleaning crews or other folks can sometimes unplug things.)
Unplug external hard drives and basically anything you don’t need to have plugged in. I once had an issue where I had checked every connection except the video cable that physically plugged into the monitor itself, and had I checked in the first place, I could have saved hours of time.
Also, if your PC has the small on/off switch in the back on the power supply (where you plug in your PC) make sure it is switched on, so the small line is pressed down, and not the power circle that is usually on the front panel.