Hmm, you know what my mother's Samsung tab did the same thing once. It was all dim and unresponsive. I don't exactly know what I did but I think I pressed the buttons for multiple configurations and times until one combo worked. I think it was the volume up and power button and was a good amount of time. Like over a minute.
This reminds me of those Chinese MP3 players I used to have sometime ago, they would die in similar fashion and would not charge or display anything.
When you plugin the device, does it show any signs of charging like the logo at the top turns to lightning bolt (I hope Samsung uses that). you also say that the device is left on until battery finishes, if it's been going on for quite some time may be the screen has some issue.
Another possibility, as mentioned above, is that the charging port of the tab might be damaged. Check if the charging point fits properly.
Connect the tab to you laptop or PC and see if it is recognized.