No I do not agree: the physical computer/system can only manifest what **limited imitation** of human intelligence it is able to BECAUSE the intelligent human DESIGNED and BUILT and PROGRAMMED it to do so. It clearly does not do so otherwise. Computers would not even exist otherwise. Human intelligence is necessary. The argument for design still stands. It is after all called "artificial intelligence" and is only a reflection, not actual independent intelligence.
Behold the chimp
You have created a circular argument. Your argument was the computer. A non-biological system. Since the computer which may evidence a "dim reflection of intelligence" does not exist on its own and did not evolve over billions of years, the operation of the computer can not tell us about the operation of the brain or intelligence of the human which created it, or of any other biological system, such as a chimp brain. You posit intelligence in the chimp. The chimp did not invent the computer, so the computer's "dim reflection" can't tell us anything about the chimp's "intelligence", other than by the analogy of intelligent design. Since the computer is a manufactured thing, its "dim reflection of intellegence" can only reflect the intelligence of its human inventors/engineers/programmers. The "dim reflection of intelligence" you see in a chimp -- whatever it actually is -- is manifestly less powerful (i.e. analytically, etc.) than that of the human-created computer. So the chimp was likely created too, but we know by other means that the chimp was not invented by humans . . . This is your argument, not mine . . . just following it a bit . . .
Let's take it one further step. In that you have basically changed your argument from intelligent design as reflected in the computer, to the existence of the soul in animals. Since, as you point out, your logic leads to that direction, rather than to the human NOT having one. That does not change whether or not God created the Universe.
As to your point about brain damage, etc. Well, human beings are not disembodied spirits. We have to operate with the "hardware" of our bodies. That's the way it is for human beings existing in space and time. We don't have the option of operating as pure spiritual beings. It makes sense that limitations in our physical bodies would affect the ability of our spirits/souls to manifest themselves in space and time.