I think I have experienced something similar on a couple of occasions. Now, I'm not sure of this but when it happened to me I think that the battery was completely flat.

Also I'm not sure what actually solved the issue but I seem to remember that I first took the battery off and then put the battery back on again.

Then I just plugged in the charger and left it like that. At this point there is no indication that the device is charging as you also describe but I believe the battery is being charged and it will again be possible to turn it on as usual after an hour or two. At least this is how I remember it :-)