Here are the pins reserved by the shield, as noted in my header files.
You may have to adjust the numbers for your DUE
/* Pins Occupied by WiFi shield
SPI occupies UNO pins
10 - SS, shield select
11 - MOSI, Master Out Slave In
12 - MISO, Master In Slave Out
13 - SCK, Serial Clock
4 - SS, Slave Select*/
I don't yet know enough about the electrical stuff to say
which pins MUST be kept clear. Keeping all of the clear
works for me, as they say.
Network protocols I do know about. I think I said elsewhere,
the example web server is not a great place to start learning.
The example code does not conform fully with the HTTP protocol
which means you are in unknown territory.
I am attempting to write a conformant web server but I am not there yet.