I read it. Who cares how improbable it is? 17 billion years and 17 billion monkeys isn't very much. I actually think you kind of missed the point of that paper (it was a geek joke), but whatever.
So no, you can't get Hamlet out of randomness, much less the entire collected works of Shakespeare, and certainly not a sophisticated computer program.
How do you logically fly from utterly improbable to impossible? It may seem to be true for you to equate the two in day to day life, but it isn't even remotely true in a mathematical sense. Mathematics doesn't use rounding errors and fudge factors (though engineers do).
That's easy: "utterly improbable" precludes you from ever being able to demonstrate that which you had the nerve to call "trivial" to provide.
You don't have 17 Billion years. The Earth hasn't even been around that long.
You've been disproven by math. Game over, man. Game over.
With that in mind, how *possible* is it for those monkeys to finish the entire play? Or how possible is it for those primordial organisms to evolve into the thousands of Earth species WITHOUT design?
I'm probably over my head here, but it would seem to me that simple results may occur with the right circumstances. More complex results may indeed be an impossibility, especially since life on Earth is believed to have originated in a finite amount of time.