Button Input not working?

From my comment : I strongly suggest you look at this excellent answer by Aldo. It shows what you are trying to do. Tap into the character motor and modify the variables therein : http://answers.unity3d.com/questions/164638/how-to-make-the-fps-character-controller-run-and-c.html

Firstly : you really should not modify the standard script. If you do, at least change the name of the script. Why? Well just imagine one day you accidentally re-import the first person character controller. Boom, in one step you have wiped out all your code, gone, overwritten, gone.

So my answer is a whole separate script (especially for future readers), all you have to do is attach it to the first person character controller.

I have changed the name of the boolean. You can use walk instead of isWalking, but just be aware by convention variable names are lowercase / camelCase. Read the commenting and make sure you understand what is happening.

 #pragma strict
 
 var walkSpeed : float = 7; // regular speed
 var runSpeed : float = 20; // run speed
 
 var isWalking : boolean = false; // boolean to show current speed state
 
 private var speed : float; // this variable stores the current speed
 private var chMotor : CharacterMotor; // store reference to Character Motor
 
 function Start() 
 {
     chMotor = GetComponent(CharacterMotor); // store reference to Character Motor
     speed = runSpeed; // start off at running speed
     isWalking = false; // set boolean to reflect speed is running speed
 }
 
 function Update() 
 {
     if ( Input.GetButtonDown( "Walk" ) )
     {
         speed = walkSpeed;
         isWalking = true;
     }
     
     if ( Input.GetButtonUp( "Walk" ) )
     {
         speed = runSpeed;
         isWalking = false;
     }
     
     // modify the character motor speed variables
     chMotor.movement.maxForwardSpeed = speed;
     chMotor.movement.maxBackwardsSpeed = speed;
     chMotor.movement.maxSidewaysSpeed = speed;
 }

Many thanks to Aldo, without his answer this script wouldn't be here because that's where I learned to do this =]

Edit : if you really really want to edit the standard script, first do as I suggested .... Rename it! , so no accidental imports overwrite all your work.

 #pragma strict
 
 var walkSpeed : float = 7; // regular speed
 var runSpeed : float = 20; // run speed
 
 var isWalking : boolean = false; // boolean to show current speed state
 
 private var speed : float; // this variable stores the current speed
 
 function Start() 
 {
     speed = runSpeed; // start off at running speed
     isWalking = false; // set boolean to reflect speed is running speed
 }
 
 function Update() 
 {
     if ( Input.GetButtonDown( "Walk" ) )
     {
         speed = walkSpeed;
         isWalking = true;
     }
     
     if ( Input.GetButtonUp( "Walk" ) )
     {
         speed = runSpeed;
         isWalking = false;
     }
     
     // modify the character motor speed variables
     maxForwardSpeed = speed;
     maxBackwardsSpeed = speed;
     maxSidewaysSpeed = speed;
 }