Sony Cybershot DSC-W5 won't turn on

I've noticed many, many, many people with similar problems, but in my case the camera won't even turn on. Nothing, nada.

Originally we had been taking some photos over many days, and on one day it just turned off, and the lens stayed extended.

We managed to ease the lens closed (much later), but since the time it stopped working it hasn't turned on again.

We noticed that it only "responds" when the batteries are taken out and put back in. After hitting the power button, the LCD briefly flashes the menu, says "Accessing..." and then shuts off. I don't think it's an issue with the lens itself; it seems to be software-based.

We've switched batteries, memory cards, but nothing is helping.

Any ideas?