sure, remove memory. and decision making, that's biochemical too. And personality? probably. Remove some impulses and reflexes and primordial pathways. Now that's the real you! What's left, though?
My comment was related to the OP comment. When you were born, you didn't have any reminiscent memory, because memory is intrinsically related to your physical brain. If you damage your brain, you could lose memory or change completely what you call "self". If you are a Christian and believe in after-life, a good way to reconcile this is downplaying the importance of memory itself (overrated). But this is related the OP's point of view (Christians believe in after-life). I, personally, don't believe in after-life, so everything you are is in your brain and memory is crucial.
FYI, I still believe in an afterlife. The bible talks about a resurrection where all will be raised from the dead for judgement. It's common misconception to think we float off to heaven or hell as disembodied souls. The difference is we will again have physical bodies, and thus have the capacity for consciousness and memory again.