Leave the device to charge 2-3 hours, and then, still connected to the charging cable, remove the the battery from the device a few seconds and reinsert it. If it boots--leave it to charge to 100% (check Options > Status for the percentage). If it doesn't reboot on the first attempt, leave it several more hours. I've had one charge for two days before it came back to life after an extreme battery depletion. Every 3-4 hours, with the device still connected to the charger, you can remove and replace the battery to see if it reboots.
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