Just to be clear, are you talking about the "Full Shutdown" thing you can do from them menus? Or just the "off" you get from the power switch?
The symptoms you're describing sound like a totally drained battery to me, and aren't uncommon at all when the battery gets totally flat.
What
would be unusual is if it managed to get there while in the full-shutdown-like-you-get-from-the-menu-option thing.
