Dead Canon A75
A complete camera failure is usually caused by a power problem. Naturally, after checking the batteries, you should inspect the metal battery terminals inside the battery compartment.
Also, many cameras (including the Canon A-series) have a memory card door with a safety interlock lever (power switch) that is engaged only when the door is completely closed.
Finally, I have learned (from a Canon camera forum at Digital Camera Resource) that there is a small fuse soldered to an internal circuit board that sometimes fails for no apparent reason with several different "A" series Canon digital cameras.
The fuse story, with photos for those brave enough to void their warranty and open up the camera, begins inside this thread,
"Canon powershot A85 spare part needed!!!"
at this web link:
You'll need to read a couple pages down to get the entire story.