Summarize this article in one sentence.
The S model has a touch-sensitive button, and may not work with a gloved finger or if you use a fingernail. Press the button with your bare finger to turn the console on. An overheating power supply is one of the most common reasons that an Xbox 360 will not start. Many people tuck the power supply away, but this can lead to heat build-up. Make sure your power supply is well-ventilated and not blocked by other object.  Unplug the power supply on both ends and let it sit for at least an hour to cool. Make sure the fan in the power supply is still functioning. You should be able to hear a faint whirring sound when the power supply is plugged in and turned on. If the fan has failed, you'll need to get a new power supply. If you get two red lights on your Xbox 360 Power button, your console is overheating. Turn it off for a few hours to let it cool down. Make sure that the Xbox 360 is placed in a well-ventilated area and that no other objects are directly next top it or stacked on top of it. There is a lot of anecdotal evidence that keeping your Xbox 360 horizontal will lead to better cooling. If your Xbox 360 is displaying four red lights, your video cable may be damaged or incompatible, or the connection isn't complete. Check that all of the plugs are connected properly. Try using a replacement official video cable to see if your problem is fixed. Sometimes you can have too many things connected to your Xbox 360, causing it to draw too much power. This is especially common with modified consoles with unofficial hard drives or other peripherals. Disconnect everything you can and try to start the console again. This failure is commonly accompanied by error code E68 on your TV. A common cause of failure for Xbox 360 consoles is bent pins in the USB ports causing a short circuit:  Examine the USB ports on the Xbox 360, both in the front and in the back. If any of the pins inside are touching each other or the casing of the port, they are likely causing a short circuit. With the Xbox unplugged, use tweezers to gently bend the pins back to their original position. Avoid using the USB port in the future if possible so that the pins don't get bent again.

Summary:
Use a bare finger to press the Power button (Xbox 360 S). Let the power supply cool. Let the console cool. Try a different video cable. Disconnect any peripherals. Look for bent pins in the USB ports.