There is always the possibility that you have one weak battery.
Buy some new AA alkaline batteries
make sure they are installed properly.
See if that works.
I have heard of this on other brands of cameras.
It usually has something to do with a weak battery and the lens extended.
Apparently the lens does not retract completely into the camera.
You might try pressing (gently) on the front of the lens barrel in an attempt to seat the lens in its parked position. Then turn-on the camera see if that worked.
Look at the gap between the rings of the lens barrel and see if one side has more space that the other. If so, apply gentle pressure to try to equalize the spacing between the rings of the barrel.
Try power-on again.
Others have reported that they slapped the side/top/bottom of the camera. They report that this does work in some cases.
Just don't over-do it.
Yesterday I attempted to use my camera, and powered it on. I then took a photo, then it gave a message "low battery"
I switched to what I thought was a fresh set of batteries (Duracell NiMH rechargeables that I thought I had previously charged a day or two before) the camera did not power on. So I assumed the batteries needed charging?
When I got home, I then inserted yet another set of 15 Minute Rayovac NiMH rechargeables, and the camera powered on, all was good so I shut it down again.
Today I went to use my camera, and now it will not power on, with any of my batteries, even after a full charge.
I searched google, and found some tips mentioning items such as if the lens was extended when the batteries were drained, or a tab on the battery door may be broken, or removing the memory card, and try powering on, etc. Nothing like that seems to be an issue, so I am at a loss to explain this.
Any help would be appreciated, thank you.