Minds depend on physical brains. Religions depend on belief in souls--essentially minds that can exist independently of bodies. But experience tells us that minds depend on brain activity to function properly.
I don't see this as a basic tenet of Christianity (that minds exist independent of bodies), and I don't think it's an obstacle for any other religion that believes in a continuation of the self after this mortal life. The information accumulated from this life that constitutes 'self' could be transferred and translated to some other kind of existence. The next 'body' could be very different from this mortal coil.
Record of failed explanations.
Religions have a historical record of making failed explanations of observed natural phenomena. The most powerful argument for gods--the argument from design--has been overturned by the discovery of evolution by natural selection. This pattern of failure has resulted in a pattern of "God of the Gaps" explanations. That is, natural explanations always trump supernatural ones.
Religion is not science and is not meant to explain the scientific aspects of this universe. Religion is about our role in this universe, our relationship with God, nature, and each other.
Record of failed revelation.
Humans have a record of worshiping false gods. If gods communicated through revelation, we would not expect to see such variety of religious belief in the world. Moreover, we would expect to find the same religious beliefs arising spontaneously in different locations, since the same set of gods (or "God") would presumably contact different people in different locations.
The interpretation of revelation depends quite heavily on the person receiving it. The light from the sun is the same, but it appears quite different when it is intercepted by a stone vs. cut diamond vs. the leaf of a plant.
Record of failed prayers.
No religious group seems to be luckier or healthier than any other. If prayer worked, we would expect to see some people of faith leading more fortunate lives than the rest of us.
Prayer raises all boats together.
Record of failed corroboration of miracles.
Religions depend on stories of miracles--events that contravene natural laws--to support religious belief, yet miracles are notoriously resistant to corroboration and verification.
Because a miracle is, by definition, something outside the bounds of science and human control, it is no surprise, and no damning evidence of failure, that miracles are not corroborated by science.
Of all the above reasons, I consider #1 the strongest, because mind-body dualism seems to underpin all religions. I do not oppose the idea of dualism so much as the belief that minds can exist independently of brains. It seems pretty obvious that our minds depend on the physical state of our brains.
Because reason #1 is the least relevant to religious faith or the existence of God, I'd say your argument is overall quite weak. Minds depending on this physical brain is not a no-brainer.
Note: None of the above reasons is intended as an absolute proof that gods do not exist. These are reasons that make me consider belief in the existence of gods to be highly implausible.
Fair enough!