Why won't camera stay on?

I replaced batteries (yes, they are inserted correctly; no Captain Obvious suggestions, please!) and the lens extended as usual when camera is on, but camera wouldn’t stay on for more than about 2 seconds. The screen remained dark. When i hooked camera to imac with the USB cable, the lens retracted, but even plugged in, the camera won’t go on. I removed the memory card but that didn’t help.