"Computer" is an observer-relative term. There is no physical property of a system which makes it a computer. A "digital computer" is just a tool made of silicon which we use to aid computation (a goal we have). There are many tools (from an abacus to a waterfall) that we can use to aid in computation.
"Computation" isn't anything other than a goal we have. To interpret the brain as engaged in it carries no information and says nothing explanatory. The sense in which a brain is a computer is the same sense in which everything is: a physical system whose state evolution can be used to aid in computation (but isnt: no one uses brains to compute).
A rock and a waterfall perform computations in a theoretical sense if you look at them right, but there's also a different sense in which a bunch of op-amps in a circuit are a computer, a bunch of hydraulic logic gates are a computer, and a Raspberry Pi is a computer, but a rock isn't a computer. In that sense, human and animal brains are computers too.
(I'm before my morning coffee so I apologize for not being able to name "that sense" properly.)
I chose waterfall by symmetry with a hydraulic computer. A waterfall is just what we call a hydraulic computer when we're not using it for computation.
I still only see an observer-relative distinction (ie., in how it is used). One can "juggle rocks" to compute.
You've said something about "inputs" and "useless when removed". Both of these are again observer-relative. Useless gives it away.
An animal isn't "useless" when its brain is removed, because it isn't our use of it which makes it alive.
Computational neuroscience could be written off by your statement that the brain is not a computer, but perhaps soften your stance and accept that that allows for applying tools from computer science to ask questions, just as physicists do.
Computational metaphors arent explanatory, they're illusory sorts of explanations (like narrative) which "satisfy" without providing a causal model (ie., a scientific explanation).
I'm not convinced they have been helpful, and mostly end up giving deeply mistaken impressions about the nature of digital computers -- rather than helpful impressions about the nature of brains.
The key is to explain using layman's terms without making false claims while trying to simplify the subject.
When people call a thing a 'computer' they mean that it can run (potentially complex) algorithms to produce outputs based on inputs, in many cases it would also be assumed that it has memory, and it would not have much in the way of direct physical interactions with the world (although it might be part of systems that have such interactions). Based on these notions, it seems very valid to interpret brains as some kind of computer, made out of cells instead of metal and silicon, and formed by evolutionary pressure instead of human engineering.
It isnt valid to interpret brains this way. An "algorithm" isnt something a physical system can "run". These are observer-relative properties a system instantiates because of our use of it.
A brain is a physical system and our model of it should be a causal model in terms of its intrinsic properties that do not "disappear" when not in use.
A digital computer is an oscillating electrical field across a piece of silicon whose oscillations "correspond" to steps in an "algorithm" but only to an observer who imposes those correspondances. The program "1 + 1" on a digital computer is some state transitions of the cpu's electrical state -- it is an algorithm only when we impose an meaning on those oscillations that they do not themselves have.
There is no physical distinction in the "waterfall computer" and "digital computer" that bares on them being computers. They are both computers in exactly the same way. We havent gone to the length of a water-to-lcd display, but there's no reason we couldnt.
Water falling over a series of moveable rocks can (easily) be arranged to display the result of "1 + 1" on an LCD (eg., bucket/pixel, with water level = intensity, pipes to handle "graphics").