I have worked on a number of these tablets and one thing that has repeatedly shown up is that the battery connector will break away from the main board. The device is so wide and the screen is flexible that the main board flexes back and forth and the solder joints crack. Then it wont make: continuous, reliable, or possibly any connection.
The most common symptom is that the screen will show the little no battery icon but in extreme cases you wont even get that.
To test for this I generally remove the back case, sometimes you can even do it with the case on, and apply some pressure to the battery terminal, in the center of the device, and see if I can get some response from the device.
If this solves it there are a few other posts on the web that show how you can repair it by re-soldering the connection. It is really small so you will need a magnifying glass and the appropriate soldering tools but it is really not that difficult.