At zero degrees Kelvin, when KE=0, there should be little, if none at all, motion among any particles in the affected, enclosed area.

According to Heisenberg, one cannot measure a particle's motion without altering its position, and vice versa. Thus, small elementary particles cannot be seen and the apparatus used in the experiment is part of the experiment since it can alter the particle's position or momentum. Additionally, it has been "proven" that travelling particles (that are about to collide or pass) "know" what the other one is doing.

Does Bose-Einstein condensation have anything to say about this?

Now, my theory: at zero kelvin, there is no momentum. Therefore, a particle has no momentum during the moment the "event" is captured at zero kelvin - time must also stop for the particles - and therefore position can be accurately measured. A few ultra-milliseconds later, a second picture is taken (the particles roam around a weeny bit after the first measurement is taken and the degrees are raised a hundredth of a degree). Now, we have two events, close together, in which the particles were "frozen" in time and in their respective positions. In the second observation. the particles have a second position or have collided, so particles' momentums between the two observation can be deduced. There you have it (a bit to long).

One problem: To observe this experiment, we need an apparatus to measure. Modern apparati, as far as I know, shoot photons and stuff which rebound back, altering the particle's position (correct me if I'm mistaken).
Because of the one flaw in this theory, the experiment cannot actually be observed using any modern apparatus (unless I'm that far behind the rest of you)...unless someone knows a way around this obstacle.