The camera does not switch on

Have you checked that the battery is fully charged or is still good? If you ruled out a battery issue then check that the terminals on the camera are clean (no build up on the terminals where the battery contacts). You can clean them with a cotton swab and some iso alcohol (wait for it to dry before re-inserting batteries).

Also your manual may have some helpful hints Canon Manual 3350

One more note: Some canon cameras have a switch that opens and closes when the battery door opens.

This tells the camera that the battery door is open and the unit will not turn on if the battery door is open (some models). This is something to consider. Sometimes when i run across canons that do not power on this door detecting switch is jammed.