VNC?
I don't think it's possible for a system to be invulnerable (unless it's like uh... unplugged, but that defeats the purpose). There's probably always a way in; it's just a matter of finding it.
In the labs at my old high school, I used to unplug my mouse/keyboard and plug them into other peoples' computers when they weren't looking. It sounds like the motions you're talking about are a bit too controlled for something like that, though.