This is interesting, and I think you've reached the right conclusion, but the reasoning is flawed. It has to be flawed, because it can be used to prove that we're not sentient either.
Just create an arbitrarily accurate digital model of a human brain and step through time. Is it sentient? If not, make it more accurate until it is. If it is, where is the sentience? It's just numbers and algorithms, right?
You could argue that sentience just doesn't exist, which may be valid, but if it does, I don't think you can get very far with a reduction-to-parts analysis.