I connected everything like in the blogpost: An Arduino Library for the ADT7310 SPI Temperature Sensor – The inability to follow simple instructions
This is not possible because there they don't use an Ethernet Shield. I asked for your wiring and not the guide after which you think you've done it. Make photos of your setup and post them. Take care that all connections are visible on the photos.
And I ask again: Are you using an UNO?
Can you check if your pin 4 is working (remove the ethernet shield, then load a sketch that is switching pin 4 HIGH and measure the pins voltage, post the results)?