MQTT vs Tinkerkit sensor Shield
I think your problem is in wiring. Ethernet shield is using SPI communication, it requires pins: SPI: 10 (SS), 11 (MOSI), 12 (MISO), 13 (SCK). Those pins must be left for the Ethernet shield. Information is from Arduino Uno description. 

Does your Arduino communicates with you after you plug-in Tinkerkit? If not, maybe you have a short in Tinkerkit shield.