There, again, I'm not so sure this is easy. We can calculate the channel capacity of a specific state. We know how many errors can kill the interaction between a sequence of DNA and another molecule in a specific environment. Such an interaction is kinetic and the downstream effect of errors are not binary. That is, the "message" doesn't arrive either whole and readable or with too much noise to be read at the destination, but, instead, a reduced message or a message with noise becomes a different, yet readable, message.
Maybe this is all simple for those who love their differential equations, but I don't think it's a simple matter to compute either the information content or the channel capacity of a DNA sequence, per se.
Agreed. But we can certainly put an upper limit on the information content,. If we say the number of combinations in DNA is 4^N, where N is the number of base pairs, then the entropy of the specific sequence can be no more than k*N*ln 4 lower than total randomness. As I've noted before, this is a thermodynamically tiny quantity; for 10^9 base pairs, it is of the order of 10^-14 J/mol K, or equivalent to the order produced by freezing about a 10 femtograms of water. If the sequence is not unique in terms of phenotype (which, as you note, it will not be), the negative entropy will be lower than the number computed above, but it cannot be higher.
We could also argue that not all the order in the cell resides in the genome. After all, a genome cannot produce a new organism unless it has the entire apparatus of the cell to work with. We could put an upper bound on this by ordinary thermodynamic measurements - just by burning the organism, for example - and again it appears the negative entropy is absolutely minuscule.
It's a sobering thought, but the human genome does not appear to be particularly complex. The Bible, I'd warrant, has nearly as much information content as any of our genomes.