CM3 Power Switch Broken?

[Flavor]

I would wonder if your LCD ribbon cable is fully connected and locked into place.
I also still wonder about the SD card image.

Is there insulation between your speaker and the circuit board?

The switch has 4 "pins" on it.  The 2 middle pins are the same.  Let us call them the common connection.

When the switch slides, it changes where it connects this common.  In one position, it connects the common to the left pin.  In the other position, it connects common to the right.

Code:

Position 1             Position 2
|----||    |           |    ||----|

Do you have a multimeter to check voltage?  When the switch is at rest, the middle/common of the switch should be close to 0v.  When you push the switch, the middle/common of the switch should become the same voltage as the battery (somewhere around 3.7v).

Here's another test.
Unplug all batteries and USB.  Tap the power button for 1 second and then release it.  Then watch the front GBA LED while you plug in power to the microUSB charging port.  Does the LED flash red very quickly?

Do you have HDMI to plug in?  If so, it can greatly help the debugging process if there is a problem with the built-in LCD.