You will indeed need to call a function (or access an public variable) on the other object. For the sake of the example, I'll assume the script with the key code is PlayerScript; but just substitute the real name below. The first thing to do is to add a function to get the key state in that script

private var gotKey : boolean = false;

function HasKey() {
    return gotKey;
}

function OnControllerColliderHit (hit: ControllerColliderHit) {
    // ...
}

Then in your door script, you just need to grab the script on the player object using GetComponent(type). Once you have the component, you can call any public function (or access any public variables, from that script.

function OnTriggerStay (other: Collider) {
    var player : PlayerScript = other.gameObject.GetComponent(PlayerScript) as PlayerScript;
    if(player != null && player.HasKey()) {
        if(door.transform.localEulerAngles.y < angleOpen) {
            door.transform.Rotate(Vector3.up*Time.deltaTime*speedOpen);
        }
    }
}

I believe this will work.

Key script

var doorKeyOpens : Transform;
private var gotKey : boolean = false;

function OnControllerColliderHit (hit: ControllerColliderHit) {

if(hit.gameObject.name == "key") {
       print("You Picked Up The House Key");
    doorKeyOpens.gotKey = true;
    Destroy(hit.gameObject);    
    }  
} 

Door script

var door: Transform;
var gotKey : boolean = false;
var angleOpen: int;
var angleClose: int;
var speedOpen: int =1000;

function OnTriggerStay (other: Collider) {
    if(door.transform.localEulerAngles.y < angleOpen) {
        door.transform.Rotate(Vector3.up*Time.deltaTime*speedOpen);
    }
}