The problem is partially a sensory one. With the brain case, we accept that we have consciousness when the whole brain is there. It's still there when we separate the parts and wire them together. It's still there when we fluke out the inputs on one side?? It's still there when all the parts are not actually connected any more?

Check this:

“Consciousness continues to confound us on all fronts — we haven’t even established what it’s good for,” Watts says. “It’s slow, metabolically expensive, and — as far as we can tell — unnecessary for intelligence. More fundamentally, we don’t have a clue how it works — how can the electrical firing of neurons produce the subjective sense of self? How can a bunch of ions hopping the synaptic gap result in the sense of this little thing behind the eyes that calls itself ‘I?’”

“One thing we have discovered is that consciousness involves synchrony — groups of neurons firing in sync throughout different provinces of the brain,” he says. “Something else we’ve known for some time is that when you split the brain down the middle — force the hemispheres to talk the long way around, via the lower brain, instead of using the fat high-bandwidth pipe of the corpus callosum — you end up with not one conscious entity but two, and those two entities develop different tastes, opinions, even different religious beliefs.”

“What this seems to point to is that consciousness is a function of latency — it depends upon the synchronous firing of far-flung groups of neurons, and if it takes too long for signals to cross those gaps, consciousness fragments. ‘I’ decoheres into ‘we,’” Watts says.