I would suggest checking to see if you have set JP1 according to the Elektor instructions--I imagine that pulls down the WP pin of the EEPROM and/or the SELFBOOT pin of the ADAU. Then I'd scope the SCL and SDA pins to check for proper data flow. If that works, I'd selfboot the ADAU and monitor the same. Possible issues I can think of: the EEPROM is inserted incorrectly, the EEPROM address does not match in SigmaStudio, your programming utility (this is not an ADI product) is not sending correct data.
ADI designed the ADAU to be programmed with their own USBi board, which you can find here:
I am not sure what Arduino would add to that process, but the USBi works quite well and is not expensive, and you can develop in SigmaStudio in real time and without setting jumpers and pressing reset buttons manually on your target board with each program upload if you have implemented the same functionality as ADI does on their eval kit -1701 board. If you can get your ADAU to work directly with the USBi, then you know the problem has to lie elsewhere, either with the EEPROM or your programming utility.