mosfet driver uln2003
There is only one remaining thing other than a misconnected or faulty part (which will be very difficult or impossible for us to diagnose). 

If you grounded pin 9 ("COM") on the ULN2003 the output voltages will be clamped at about 0.7V which will be insufficient to turn on the MOSFET. I suspect that is the case, since you've shown two wires to the ULN2003 that are grounded. Of course "E" must be grounded- that's the emitters of the Darlingtons. 

Leave "COM" open, or connect it to +5V. It's there to clamp inductive loads to a higher voltage such as the supply voltage (or higher in some cases). Since you do not have an inductive load on the ULN2003 it is not required. 

To diagnose, in general, follow the signal through your circuit and record what is going on. Verify the input voltage to the ULN2003 off and on. Verify the output voltage is what you expect (about 5V and 0.8V for on and off). And finally verify the voltage across the motor.  

And, as others have stated, you can drive this particular MOSFET just as well by connecting the 10K directly to the microcontroller- in fact you can reduce the resistor to a few hundred ohms and drive it better. You only need the ULN2003 if you intend on using a non-logic-level MOSFET and a higher supply voltage (such as 12V) for the gate driver.