Assuming you know that the battery in the camera does have power...
There are a couple of micro-switches that will prevent the camera from powering up (or if tripped... will cause the camera to power off immediately.)
One is on the battery compartment door.
The other is on the memory card door.
The doors themselves have small tabs which, when closed, will engage the switches. If the door(s) do not fully close, or if the tab is damaged then the switches might not be completely engaged.
I've tested a few cameras by _very_ slowly opening each door to determine how far open it can be before the switch disengages. On some of my cameras it's quite a bit. On other camera bodies... the switch is barely engaged only when the door is fully closed.
If you inspect the door and door frame you should see the tab. You could test by taking a toothpick and just "gently" (do not jam in) press the tab (with camera in the "on" position) and see if the camera comes to life.
If you have a bad switch or a mis-adjusted switch (not fully engaging) then you'd probably need to send it to Canon for service... but at least then you'd know what you are dealing with
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