I have the Arduion DUE and the Ethernet shield in hand and plugged together. Analog inputs 6 and 7 are obscured by the shield. I selected the DUE for the analog sensors.
How you resolved this problem?
I posted, could not find it, added to another post, then found this. The answer is found here:
https://forum.arduino.cc/index.php?topic=585058.0
My apologies for the dual posting.