I am making a 2D game, and when I hold the key "w", the player goes forward, but when I hold both "w" and "a", the movement stops completely, when I want it to go forward, while shifting to the left.

Here is my script:

var speed = 4;
function Update() {
    // Make the character walk forward if "w" is being held
    if(Input.GetKey("w")) {
        rigidbody.velocity = transform.forward * speed;
    }
    //  Stop the movement if "w" is not being held
    if(Input.GetKeyUp("w")) {
        rigidbody.velocity = transform.forward * 0;
    }

    // Make the character walk forward if "s" is being held
    if(Input.GetKey("s")) {
        rigidbody.velocity = transform.forward * -speed;
    }
    //  Stop the movement if "s" is not being held
    if(Input.GetKeyUp("s")) {
        rigidbody.velocity = transform.forward * 0;
    }

    // Make the character walk left if "a" is being held
    if(Input.GetKey("a")) {
        rigidbody.velocity = transform.right * -speed;
    }
    //  Stop the movement if "a" is not being held
    if(Input.GetKeyUp("a")) {
        rigidbody.velocity = transform.right * 0;
    }

    //Make the character walk right if "d" is being held
    if(Input.GetKey("d")) {
        rigidbody.velocity = transform.right * speed;
    }
    //  Stop the movement if "d" is not being held
    if(Input.GetKeyUp("d")) {
        rigidbody.velocity = transform.right * 0;
    }
}

PLEASE MAKE THE CODE BETTER! I AM NEW!

EDIT: Here is a video to show my problem. http://www.screenr.com/3oxH

Here is the newest code:

var speed = 4f;
function Update() {
    if(Input.GetKey("w")) {
        rigidbody.velocity = transform.forward * speed;
    } else if(Input.GetKey("s")) {
        rigidbody.velocity = transform.forward * -speed;
    } else if(Input.GetKey("a")) {
        rigidbody.velocity = transform.right * -speed;
    } else if(Input.GetKey("d")) {
        rigidbody.velocity = transform.right * speed;
    }
    if(Input.GetKeyUp("w")) {
        rigidbody.velocity = transform.forward * 0;
    }
    if(Input.GetKeyUp("s")) {
        rigidbody.velocity = transform.forward * 0;
    }
    if(Input.GetKeyUp("a")) {
        rigidbody.velocity = transform.right * 0;
    }
    if(Input.GetKey("d")) {
        rigidbody.velocity = transform.right * speed;
    }
    if(Input.GetKeyUp("d")) {
        rigidbody.velocity = transform.right * 0;
    }
}