Your code looks fine, but it seems to not work for some reason.
I got what I wanted by modifying your code into this:
Code:
import flash.display.*;
import flash.events.*;

var buttons:Array = [box1, box2, box3];
var current:MovieClip = null;

box1.addEventListener(MouseEvent.MOUSE_DOWN, buttonPress);
box2.addEventListener(MouseEvent.MOUSE_DOWN, buttonPress);
box3.addEventListener(MouseEvent.MOUSE_DOWN, buttonPress);

function buttonPress(e:MouseEvent):void{
  box1.gotoAndPlay("clickthis");
  box2.gotoAndPlay("clickthis");
  box3.gotoAndPlay("clickthis");
  box1.removeEventListener(MouseEvent.MOUSE_DOWN, buttonPress);
  box2.removeEventListener(MouseEvent.MOUSE_DOWN, buttonPress);
  box3.removeEventListener(MouseEvent.MOUSE_DOWN, buttonPress);
  box1.addEventListener(MouseEvent.MOUSE_DOWN, buttonPress2);
  box2.addEventListener(MouseEvent.MOUSE_DOWN, buttonPress2);
  box3.addEventListener(MouseEvent.MOUSE_DOWN, buttonPress2);
}

function buttonPress2(e:MouseEvent):void{
  if (current != null){
     current.gotoAndPlay("out2");
  }
  current = MovieClip(e.currentTarget);
  current.gotoAndPlay("over2");
}
Still no idea why your code won't work as it seems to make sense to me.

I have one problem though, not sure if you could help me with it, on my contact us page, I made a contact form, but for some reason I can't click in the input text boxes. I did embed the font already.

Any ideas?

Appreciate all your great help,
SK