I think you may want to draw a GUI Texture with the size of the screen and asign the movie texture to it with a scale mode = stretch to fill, use the following ( i guess) :P

GUI.DrawTexture(Rect(0,0,Screen.width,Screen.height),MovieTexture,ScaleMode.StretchToFill);

then play the movie texture using MovieTexture.Play();

you may also want to set Screen.fullScreen = true;

and hide the cursor using Screen.showCursor = false;

and when Escape is pressed and released you may want to re-show the cursor and minimize the screen to its original location:

function Update() {
    if (Input.GetKeyUp(KeyCode.Escape)) {
        Screen.showCursor = true;
        Screen.fullScreen = false;
        // in webplayer the fullscreen mode is automatically escaped when "Escape" is pressed
   }
}

i can't test this since i don't have unity pro (so apologies if i'm answering out of turn), but this page tells how to set it up:

http://unity3d.com/support/documentation/Manual/Video%20Files.html

you should be able to create a new camera and a cube off screen from your main camera. scale the cube to fill the screen space of the new camera and attach the movie texture to it. when your trigger script fires off, disable the main camera and then activate the new camera. through that same script, tell the movie to start playing. that should get you an full screen cutscene effect.

To let your player run in full screen, set Screen.fullScreen to true.

Humm just a shot in the dark, I would create a plane with a movie texture and place it right in front of the camera. here is the pseudo code.

On each tick - Convert screen pos (width/2, height/2) to world position using ScreenToWorld() - translate the plane with the texture to the world position above - set plane direction to -camera.forward

so no matter where how the user moves he will always see the video in front of him :)

hope its clear...

Can you write the full script please?