So here we have two chemicals working together to create something, with DNA being the information, while RNA can be seen as the language interpreter.
Both these statements are only true to the same extent that "the sun is a bit like a campfire" is true. And your reasoning is akin to you referring to God as "our father" and me going "WTF?!? God had sex with my mum?" - it's taking a metaphor used to simplify and explain, and treating it as reality.
Since a RNA virus is a single chromosome then isn't logical to think that since we have 23 chromosomes X2 each parent that our chromosomes are actually RNA viruses linked together with all of their information put into DNA storage?
No not at all.
Our chromosomes are nothing like a viral "chromosome" (and, frankly, I think it's an abuse of the term to describe a virus as having one). As others have pointed it's DNA, but there's much than that. Each of our chromosomes is vastly larger than an entire viral genome. Our genes organised in a quite different manner (viruses often have overlapping genes, both on the same and opposite strands - this almost never happens in our genome - and our genes are organised into introns and exons, viral genes aren't) and code for very different proteins.
Bodge 23 viral genomes together and you'd just get a confused viral genome, you wouldn't get a functioning organism with genes for key functions such as membrane synthesis, cytoskeletal organisation and DNA replication and translation.
But that's pretty much an aside to the central reason it makes no sense: it doesn't match in the slightest to our evolutionary history. We may have 23 chromosomes, but we surely didn't evolve from creatures that did. In fact, looking at our Eukaryotic "cousins" it becomes apparent we almost certainly evolved from organisms with a single chromosome, composed of DNA and arranged in a similar way to our own with many, many similar genes. Stretching out of our domain and into the Archaea and Bacteria, and we again find a single DNA chromosome.
There is, actually, some reason to think that DNA was acquired by cellular life from viruses, but it certainly didn't happen in the way you suggest.
Can science identify each chromosome for what it does?
Re: Our genome is not a collection of viral genomes
I read that viruses are pure nucleic acid and they are everywhere in the biosphere. How is that different from our DNA that is made of nucleic acid?
Viruses aren't made of pure nucleic acid, they also have protein elements. Viroids are pure nucleic acid, and virusoids can be. The nucleic acids involved in the virus genome can be RNA or DNA. But what they're made of is a pretty poor measure of what they are; consider that all atoms are composed of neutrons, protons and electrons - would you consider that to mean that all atoms are the same? All molecules?
The differences between the genomes are much more profound that the chemicals they are composed of.
A retrovirus that was involved in making the placenta in mammals had to have a complete sequence of genes in order to accomplish it. Correct?
Complete for a retrovirus, yes. Which means it lacks the genes required even for its own replication, as well as the genes required for any of the functions of a living cell, yet alone a living animal.
The protein(s) that allow the formation of the placenta that mammals likely acquired from a retrovirus allow the formation of synctia (cells conglomerations with one membrane and multiple nuclei). These protein(s) act by modifying existing structures and processes, they do not code for new structures.
(edit) You seem to have become particularly influenced by viral involvement in the placenta. And it is a remarkable finding but consider this: the reason it is remarkable is because its very rare. Almost everywhere we look we do not find evidence of viral involvement.