Arduino original motor shield can not supply enough torque to the motor?
According to the motor shield page: 


  To avoid possible damage to the Arduino board on which the shield is mounted, we reccomend using an external power supply that provides a voltage between 7 and 12V. If your motor require more than 9V we recommend that you separate the power lines of the shield and the Arduino board on which the shield is mounted. This is possible by cutting the "Vin Connect" jumper placed on the back side of the shield. The absolute limit for the Vin at the screw terminals is 18V. 


According to you:


  I disassembled an electric screw driver which came out with a 4.8 v battery pack and a 4.8v specified DC motor.
  
  I connected battery pack to the Vin and Ground pins of the motor shield, and connected the DC motor to A channel of the shield.


That's a lot less than 7V.



Also, from the motor shield page:


  Max current   2A per channel or 4A max (with external power supply)


How much current does your screwdriver use?