If it lights up, its not your on/off switch, but if you want to check, you can hook up your rest button to the on/off power pins on the motherboard and if you don't have one, use a small flat bladed screwdriver to short the pins.
If it lights up its not your power switch. It sounds like your power supply or your motherboard, do the hard drives/ fans spin when you press the power button and do they stay on after it "turns off"?