Here:

fuction Start() { 
    Screen.lockCursor = true;
}    

function FixedUpdate() {
   // Turn
   var h = Input.GetAxis("Mouse X");
   var v = Input.GetAxis("Mouse Y");

   rigidbody.AddRelativeTorque(0, h * 20, v * 20);
   // Other way you may like
   //transform.Rotate(0, h * 20, v * 20);

   // Thrust only if Space is held down
   if (Input.GetKey(KeyCode.Space)) rigidbody.AddForce(transform.forward);
}

Also if transform.forward doesn't work try transform.right

Oh and if you want to be able to rotate:

    var rotateAmount = 5.0;
    function Update() {
       if (Input.GetAxis("Horizontal") < 0) { transform.Rotate(rotateAmount, 0, 0); }
       else if (Input.GetAxis("Horizontal") > 0) transform.Rotate(-rotateAmount, 0, 0); }
    }

To rotate use left/right arrow keys or A/D

This is pretty much a duplicate question (except for the mention of mouse/space bar for the controls), so see this answer for more detail about how to implement flight physics in general.

To read the Mouse movement, you'd want to lock the cursor, and use Input.GetAxis to read the horizontal and vertical movements of the mouse, like this:

var x = Input.GetAxis ("Mouse X");
var y = Input.GetAxis ("Mouse Y");

You'd then want to use the "x" variable as the basis for the amount of torque you apply to control banking (as mentioned in the answer linked above), and the "y" value to control the amount of torque applied for *pitch control.

To read whether the space bar is currently pressed, use:

if (Input.GetKey(KeyCode.Space)) {
    // space is pressed - apply force here
}