I know with my SX200is there is a very small microswitch underneath the battery cover. If the cover is not closed correctly, the cover is damaged or the microswitch prong is damaged, this prevents the camera being turned on.
In this sort of situation, replacement of the cover and or microswitch would be the solution. Or repairing the cover. Also I found bodging a way to keep the switch pressed in, did it for me. But be warned that you could accidentally switch it on with out the cover closed and could damage the cover more during use.
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