Arduino Due Digital Inputs without Response
A good practice is to set the pin mode for all the pins used by the sketch. 

void setup() {
    Serial.begin(115200);
    while(!Serial);
    pinMode(34, INPUT);
    pinMode(35, INPUT);
    pinMode(36, INPUT);
    pinMode(37, INPUT);
    pinMode(LED_BUILTIN, OUTPUT);
    Serial.print("Test");
}


The Arduino AVR core does set the pin mode to INPUT by default but the Arduino SAM core does not. The SAM MCU is much more advanced and allows turning on and off the ports, and a lot of other functionality. 

Cheers!