Thank you all for your criticisms. I now see that the argument from reason is probably flawed in two ways:
(1) There is no real way to draw a distinction between a concept and that same concept physically encoded.
(2) Computers are analogous to human reason in some ways, and since computers are entirely physical, it is possible that human minds are also entirely physical.
Also, @John_Harshman pointed out – rightly – that something with mental properties may not necessarily be personal. So this is a bad argument for a personal God.