I do have some neuroscience under my belt. I just happen to be half asleep.
Again, I think the answer lies in the understand that there isn't necessarily a definite line between conscisouness and not-consciousness, or between awareness and not-awareness, or between sentience and not-sentience.
Ozymandias' clever example with circuits makes the assumption that if consciousness were to develop, it would do so at some critical point. It is easy make the notion that the addition of just one more wire, or just one more sensor, or just one more switch or capacitor or resistor would magically add consicousness, because, in all likelihood, that is a silly thing to accept.
However, I don't think that in any way serves as proof that something like a computer could be conscious in the way that you or I are. Is it not more reasonable to assume that there is a continuum, where there are points clearly not sentient, points clearly sentient, and an ambiguous middle ground? I see no reason not to accept a gradient of consciousness- we see it between species, and even within our own species, both between individuals, and at different ages.
A fertilized egg is not sentient, but you and I clearly are, and I don't think there was ever an instance where BAM we became sentient.
Sentience isn't a boolean property.
I am quite confident that a computer could be equally conscious and sapient as humans are, or significantly more so, if one gives it more processing power.
There is no reason a sufficiently powerful supercomputer couldn't fully simulate a human brain, assuming it had enough processing power to calculate the interactions between all the neurons and all the chemicals.
The human brain is, when you strip away any mystical notions about the soul and all that, a glorified computer of biological origin.
It is silly to put computers in one category and brains in another and to claim that they are fundamentally different things. The only main differences are in how powerful is the strongest example of each the world has seen thus far, and what they are made of. That's it.
We could, given time, resources, and delicate instruments, build a silicon equivalent of a human brain, and it would be just as sapient.
A sufficiently well devised (or evolved via genetic algorithm) computer program would also be easily capable of sapience.