ITG-3200 with Leonardo

I checked the data sheet for the atmega32u4 and double checked the wiring.

Wo where did you connect the I2C then? You should have checked the schematics of the Leonardo, the datasheet of the ATmega32U4 does make sense when you know where the Leonardo pins are routed to. Again: show us your wirings!

I have the pull-ups enabled.

What does that mean? Do you have the internal pull-ups enabled?

But, I have a total of four i2c devices on the circuit board.

What devices are on the circuit board then? We know of exactly one yet. Are all 3V3 devices or do you have 5V devices too?