Your power switch has probably failed. You can do one of the following:
1) replace it if you can find a replacement
2) send it to HP for repair
3) (If the case also has a reset button) Remove the front cover and disconnect the reset button switch. Then move the power switch's wires to the reset button's switch. Then use the reset button to start the computer
4) on the motherboard, swap the power switch wires with the reset button wires. Then use the reset button to start the computer.