The blinking amber power button or also called Orange Light of Death is a common problem for Dell Desktop. The reason would be the electrical faulty on the Motherboard, front panel or Power supply. However most of the time the trick is to push the black button (of the Power Supply) twice.
4 steps with pictures:
1. Long press the blinking power button of the front panel until the orange light goes away.
2. Locate the black button (of the power supply on the back panel) and long press until you see a flashing orange light on the power button. You also could hear the sound of the CPU fan.
3. Release the button, and now long press it again (about 10 seconds).
4. Turn on your computer by pressing the power button and it should work.