Pull the plug. Open the case and trace the wires form the front panel to the motherboard. If you have a manual for your motherboard it will help you identify the power switch wires. Carefully remove the wires, if you have a Reset switch, carefully remove these wires as well.
With the case still open, plug in and using a small screwdriver short out the power pins briefly. If PC starts then your power switch is broken, quick fix, use the reset switch by connecting reset wires to power pins.