Atheism vs. God's Existence

[AAA]

Well DNA sequences are highly irregular. Also, the structures in cells work together extremely efficiently meaning they are non-random and clearly purposeful.

By highly irregular, I take it you mean they have a high degree of nonuniformity or variation.  This is known as having high informational entropy according to Shannon's theory of information.  According to which, such structures deviate from that which would be expected by chance.  So this "highly unique" characteristic amounts to little more than a measure of how likely the structure is to occur  by chance.

Anything can happen by random processes, it's only a matter of how likely they are to occur by chance.  A horse could materialize in my living room.  There's nothing preventing it from happening by chance, just that it's highly improbable.  So the only thing you can realistically mean by "non-random" is too improbable to occur by chance.  Again, this is just a judgement based on the probability of a structure occurring by chance.

I don't know what "clearly purposeful" means.  Purpose relates to having a goal in mind.  How you can say that any biological structure has a 'clear' end in mind is simply more question begging language.  Perhaps structures have an end in mind, perhaps they don't.  Regardless, the appearance of a thing does not in itself dictate that there is such an end in mind.

So what your criteria boil down to is saying that a particular biological structure is too improbable to have occurred by chance.  But people who suggest abiogenesis and evolution are responsible for these structures aren't claiming that they occurred strictly by chance.  So your criterion embed a false dichotomy between chance and design.  Your criteria are little more than a claim as to how probable these structures could occur by natural process.  Claiming that some structure is 'too unique' or 'non-random' is simply saying that you don't believe evolution and / or abiogenesis can account for them.  That's nothing but unabashed incredulity.  Your incredulity, or anyone's, isn't an objective feature of a biological structure.  It's simply a subjective opinion.

Yeah, you're right that shannon information is just a measure of probability, but the information in DNA is not only improbable. It also has the impressive ability to lead to functional enzymes. 

It's pretty clear that there is an end in mind when glucagon binds to a membrane receptor. It leads to the activation of a G-protein, which activates adenylate cyclase, which produces cAMP, which activates protein kinase A, which activates phosphorylase kinase, which activates glycogen phosphorylase, which degrades glycogen into glucose so the body can respond to low blood glucose. It absolutely has a goal in mind. Obviously cells aren't conscious, but there is intention. I don't think it's subjective opinion to say that the cell intends to break down glycogen when glucagon is present.

And I know that natural selection is not a random process. I was saying earlier that natural selection can theoretically lead to design without designer, but everyone disagrees with that on account of the word design. They will disagree that natural selection is a designing force, but I think it obviously is (although I don't think it has the capacity to lead to what we see in living systems).