Motor does not move with 4 batteries
In the future, please detail your attempts at solving the problem so far so we can help you better.

Approach the issue as methodically as possible. I don't know how familiar you are with electronics, so please excuse me if you think some of these questions are basic:


Ensure that the servo motor works first without any other motors or
sensors connected to the Arduino Sensor Shield (have you used this servo motor before?)
Ensure that your GVS wiring is in the correct order. Servos come with a 3 way socket that plug straight onto the Sensor Shield: G goes to the Brown or Black wire, V goes to the (middle) Red wire, S goes to the Orange wire. The good news is as the +5V is in the middle, things will not blow up if you put the 3-pin plug on the wrong way. The servo just will not work until you plug it in correctly.
Is the Arduino Sensor shield working correctly. Does the LED pin work? Do other signals sent from the board work? 
Remember that servo motors work differently to normal DC motors. You need to use Pulse Width Modulation to set the position. If you have never done this before, you will find the Arduino Servo Motors page useful. Also, you will get some excellent understanding and code from this Adafruit page. It is for a different Arduino shield, but the principles are the same.