AKA Gödel's theorem in English.

Lavengro:  Assume for a moment that reason may be flawed (pace: see my response to your next point); then no "check" which uses reason can be used to validate reason, and I can't imagine a check which doesn't use reason. Certainly, "my conclusions are consistent with reality therefore my premises and my reasoning are correct" does: the "therefore" gives it away.

Suppose a computer program were written that checked any computer program for bugs. If it checked itself and reported "No bugs" would that mean it was flawless? No, because its own bugs may have missed its own bugs.  So with using reason to check reason. (As an aside, it is trivially easy to prove that no program can be written which will exhaustively check programs for infinite loops.)

"Besides, since you and I have agreed on my assumptions, reason IS a valid tool as far as this conversation's concerned."

But what if reasoning from your assumptions leads you to a conclusion that your assumptions are false? Then either your assumptions are indeed false or your reasoning is flawed (or possibly both). Your reasoning has led you to the conclusion that "reason is the product of quantum-random or deterministic brain events."

Do you maintain that a conclusion can be valid (except by coincidence) if there's any randomness in the reasoning-process that produced it?  If not, your assumption about reason being valid is not true.  If you do, please justify this position.

To see that a conclusion must (except by coincidence again) be invalid if it's the product only of determinism is not quite so easy. I usually try to demonstrate it by saying, "You only think that because of the way your brain's wired."  I also point out that the man who sees pink elephants at the foot of his bed also has a (n alcohol-rotted but) deterministic brain; and that the woman who thinks she's a fried egg has a deterministic brain which is affected by the tumour growing against it.  Both these (admittedly pathological) brains illustrate that reason may not always be a "valid tool."L