With that said there are things about computer programs that are hard problems in human biology (and note the analog is really more of an OS to an animal -- the animal is a set of processes, not just one process). I can easily use libraries in my current program. Transplants are still non-trivial in humans. I can kill my shell and it will come back. I can even hit an unrecoverable error, reboot and things will usually still work fine. I can probably remove half of the files on my compuer and it will still work fine. I can hibernate my computer, store the state and send it to different piece of hardware. I can take an image of my machine and clone it to 100 other machines. I can add new features and upgrade my OS -- generally can't do that to my body -- at least not in any satisfactory way.
Sure there are some animals for which there are non-necessary components, just like in operating systems. But if you remove a heart or the lungs or the brain from most animals -- they'll die. Cancers can kill most animals -- there's no real equivalent to operating systems. There is generally nothing that will flat out kill an OS.
PS: Don't forget your DNA is a single program that's been running continually for over 3 BILLION years because at no point did any of your ancestors die before having offspring.
The biggest problem behind human transplants is that our defense mechanisms (which is a hard problem in computing!) will kill the foreign material. So it's a trade-off, not a hard problem.
In any case, the real difference between biological DNA and programs is the latter is designed to be modified in a _directed_ way. You could think of DNA as a highly compressed program which is modified _in its compressed form_. In evolution, changes are made randomly, so this isn't really a problem - if anything, the magnification effect is a good thing. But in computer programs, we know what we want to change, and don't want to have to make several million random changes to try to find one that brings us closer to the goal. And so computer programs are more brittle - small changes have small, predictable effects - while human DNA is more flexible, but at the expense of predictability.
And on flexibility of the human source code -- sure a small change results in a cow. But a small change in Windows (default registry settings) can make Windows start in its standard shell, command line, safe mode, Media Center mode, etc...
While I can be in awe of the complexity and power of living organisms, I don't think its all that useful to compare them to programs -- at least not based on our current understanding of biology.