It's a "Momentary Switch". I checked out how it works with my ohmmeter, and compared the switch I bought with a known good switch on another computer. The button is spring loaded, and lets power flow through the switch when the button is depressed. When the button is released, no power flows through the switch. If the button is held down for an extended period of time, then the computer shuts off. The motherboard senses a surge of momentary power when the button is pressed, and turns the computer on. If the connection stays on, then the computer shuts off.
You need to drill a hole somewhere for the switch to be mounted, and solder the wires onto the switch. The switch cost $2.49 dollars. I didn't want to buy a new case.