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.
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.