If the power supply unit is not malfunctioning, it is probably the motherboard. There is one thing you can try, it is not always recommended but has worked for me in the past. Leave the power supply plugged into your outlet, and unplug the main supply from the power unit to the motherboard, while you still have electricity running to the power supply, plug the main supply line back into the motherboard, essentially jump starting the motherboard. Let me know what happens at this point and will go from there.
Keep in mind, it is not always recommended as you can fry the motherboard trying this, but if you are already having issues to the point of not being able to reach the BIOS and or getting the beeps and tones to tell you what the problem is, then this will not matter much to try.