OK, lets start at the outlet your system is plugged into at the wall plate. Double check with a lamp is the outlet good? Then try plugging into the surge/power strip is the light lighting? If we get to that point we know we have power ;-} If you have a service tester (a little device you plug in with lights) you might want to checkout your ground and the polarity of the outlet. Outlet tester
Do you have a spare power cord that you can swap out? While Apple has a round rim a common IEC cord from a WinTel PC will do in a pinch. Otherwise with a Ohm meter you can check continuity of the cord (end to end) and with a DVM with care you can see if power is getting though. Remember you can get zapped here if you're not careful! While these two test can at least verify the cord works it don't prove the connections are good at the matting services of the plug or the socket where a spare cord can.
Now try pressing the power button and holding it a good minute you should hear the fan kick in if not the power supply is not working or the connections are not correct to the power supply or the logic board. Review steps 12 & 13 in the IFIXIT guide Power Supply Replacement.