I see. Anyways, there are multiple possibilities here, such as a faulty power button, power supply, or motherboard.
There's a very simple way of bypassing the case's power button and turning it on directly - simply disconnect the power button's cable from the motherboard's front panel headers, and then short both of the pins with a flat bladed screwdriver (touch em both at once for a moment with the tip and release) and see what happens. Do note that in most cases, the power button's cable would be using green/white or green/black wires. You could also lookup your motherboard's PDF manual to give you more specifics if needed. If it turns on, you could just put the reset button's cable in there instead (that way the reset button would be...