Don't use startDrag and stopDrag. Instead use something like this:
var myMC:MovieClip = new MovieClip();
myMC.graphics.beginFill(0x00ff00);
myMC.graphics.drawRect(-50, -50, 100, 100);
myMC.graphics.endFill();
myMC.x = myMC.y = 50;
addChild(myMC);
myMC.addEventListener(MouseEvent.MOUSE_DOWN, startMotionHandler, false, 0, true);
function startMotionHandler($evt:MouseEvent):void {
myMC.removeEventListener(MouseEvent.MOUSE_DOWN, startMotionHandler);
stage.addEventListener(Event.ENTER_FRAME, handleMotion, false, 0, true);
stage.addEventListener(MouseEvent.MOUSE_UP, stopMotionHandler, false, 0, true);
}
var damping:Number = 8;
function handleMotion($evt:Event):void {
myMC.x += (stage.mouseX - myMC.x) / damping;
myMC.y += (stage.mouseY - myMC.y) / damping;
}
function stopMotionHandler($evt:MouseEvent):void {
myMC.addEventListener(MouseEvent.MOUSE_DOWN, startMotionHandler, false, 0, true);
stage.removeEventListener(Event.ENTER_FRAME, handleMotion);
stage.removeEventListener(MouseEvent.MOUSE_UP, stopMotionHandler);
}
Just put this code on the first frame of a new, blank FLA and run it.