As Robert noted, you will need a second camera, or battery, to figure out if it is the camera or the battery. Seeing how the charger is inidicating the battery is fully charged, my gut instinct says the camera is the problem.
The camera may have a switch associated with the battery cover door, which makes sure the door is closed by preventing the camera from turning on. Make sure you battery door is closed. Likewise, make sure the memory card door is closed. Look inside of the battery compartment for foreign objects, or bent pins.
Also, be sure to only use a genuine Canon battery.
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