This article explains how to turn on an Apple Mac Mini desktop computer. It also describes what to do if that doesn't work.
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To turn on your Mac Mini, simply find and press the power button.
Locate the power button on the back of your Mac Mini. It’s on the right side (from the front) next to the power port. It’s a round button with a power symbol on it.
Press the button and wait for the system to boot. Although you may not hear anything other than the startup chime, look at the front of your Mac Mini and see if there is a power light in the lower right corner.