Koepel:
You have solved the trouble with the Ethernet shield : http://forum.arduino.cc/index.php?topic=414399.0. Nice !
I had the SD card inline when I had this problem last weekend - hence my fustration - the Ethernet worked when connected by itself, and it works for the SD card by itself.
But it is not happy when connected together. This was my issue last week.
Koepel:
I think you have run into the MISO trouble, because the SPI bus is not well defined. The I2C bus is better defined.
The Arduino Mega 2560 is a 5V board, and the W5500 chip and SD memory are 3.3V. Are you sure that those modules are compatible with 5V. You must be sure that they are. A SD module that is compatible with 5V often has a level converter on board.
Then there is the MISO trouble. The SPI bus uses a single MISO, that is the data from the module to the Arduino. MISO = Master In - Slave Out. When a module is not selected, it should keep its MISO floating, so another module can use it.
That is often not done. Many modules will work when only that module is connected to the Arduino board, and do not allow any other module on the SPI bus. I know, it's dirty, it's bad, it's cheap, but that's how it is with many modules.
Often pin 10 is used for chip select for Ethernet, and pin 4 for SD.
It is best to set 'SS', pin 53 as output, and set all chip selects to HIGH (HIGH is not active) before using the SPI bus.
The ethernet is a 5v module, and the sd card is a 5v module as well.
The SD card came from Ebay - see here EBAY
The SD module was only $1 AUS and the Ethernet was about 6 USD - quite a lot different than the adafruit at $33 USD or about $55 NZD
I have set pin 53 as an output, and I have set all Chip Selects to High.
I read an interesting article on Hackaday
about using a Pull Up resister on the CS lines - but this ended up making nothing work for me at all.
So at this time I am still a bit lost - could the SPI bus speed be an issue?
I also noticed that even having the SD library code in the skectch without the SD module connected stopped the Ethernet module from working.