I've had to charge a totally dead reader before, using the USB cable and a computer (it was before I got a PSP charger). The way that seemed to work was to plug it in for a couple of hours, then try to boot the device. The device won't boot at all when the battery is totally dead, but it doesn't want to turn the light on until the device boots. If you let it charge for a couple hours there will be enough power for the device to boot, then you can go ahead and let it stay plugged in to your powered, non-hibernating computer overnight. It should be ready to go in the morning.
If you try to boot the device and it starts but then shuts itself off, keep it plugged in a little longer before trying again.
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