I'm running the the older (december) release software. However when I tell the device to switch off, and it shuts down. With the case on it does not come back on when pressing the button.

If you have a box that you can do it with. Connect via wifi to a network and then ping the 770, keep the ping going while you put the case back over the screen. If the ping does not fail, it means that you're 770 doesn't see the case when it's on, and it's not going into stand by (you can probably test this by looking in the 1mm gap between the case and the unit to see if the screen is lit).