The big computer is part of a long term experiment in quantum mechanics. They're messing with probabilities. This explains the number of improbable occurences.
I think Desmond is not only running the system, but an integral part of it. I think he's either unusually lucky (like Walt), or psychic to some degree (like Walt may be).
The others want Walt to run the machine themselves to their own end.
I suspect there may be other hatches, or entrances.