When you turn on your camera, check that the red light next to the power button illuminates. The rid light should be lit when the camera is on. If the red light is not illuminated, a faulty battery may be the cause of the problem.
If you camera will not turn on, check that the battery is charged. Try replacing the batteries. If the battery is unable to charge, order a replacement battery.
Your camera may actually be on, but the screen may be not displaying correctly. If the batteries are not the problem, your screen might be at fault. Try replacing the screen.
Canon PowerShot A2200 Troubleshooting