Disconnect the power-cord from your computer, and press-and-hold the power button for 5 seconds.
Reconnect the power-cord. Do you hear any noise, such as a fan briefly spinning, then stopping?
Do any lamps on the computer light up?
Some motherboards have a lamp that lights-up when the power-cord is reconnected.
When you press the power button, do you hear any fans start to spin? Any noise from the disk-drive, as it spins up?
It might be time to take the computer to a local computer technician, for more trouble-shooting.