When the Due boots up it goes into a infinite loop looking to initialize the USB bus. It presents itself to the Android which then pops up the dialog asking for permission to use it. Once that is established it keeps looking for data incoming or outgoing and sends it off.
The best test I can think of is check the temperature sensors. If they’re working but the HD Tuner isn’t then it’s not the Android-Arduino connection, but the Arduino-HD Tuner connection, likely the bad cable you have. The white and yellow wires are the serial port wires, without them no communication can happen.