Solution 1:

If you'd be happy with the lid open but the machine thinking it's closed…
You can usually fool a laptop into thinking its lid is closed by placing a magnet somewhere on the front edge of the keyboard surround. So long as you don't have an old spinny rust HD near that spot, all will be fine.
You can probably detect the location by using a paperclip on the top edge of the screen, then place the magnet on the opposite face, as if closed.