If you think that humans are nothing but Turing machines, why is it morally wrong to kill a person but not morally wrong to turn off a computer?

Your question has the form:

If A is nothing but B, then why is it X to do Y to A but not to do Y to C which is also nothing but B?

This following question also has this form:

If apple pie is nothing but atoms, why is it safe to eat apple pie but not to eat napalm which is also nothing but atoms?

And here's the general answer to that question: the molecules which make up apple pie are safe to eat, and the molecules which make up napalm are unsafe to eat. This is possible because these are not the same molecules.

Now let's turn to your own question and give a general answer to it: it is morally wrong to shut off the program which makes up a human, but not morally wrong to shut off the programs which are found in an actual computer today. This is possible because these are not the same programs.

At this point I'm sure you will want to ask: what is so special about the program which makes up a human, that it would be morally wrong to shut off the program? And I have no answer for that. Similarly, I couldn't answer you if you asked me why the molecules of apple pie are safe to eat and the those of napalm are not.

As it happens, chemistry and biology have probably advanced to the point at which the question about apple pie can be answered. However, the study of mind/brain is still in its infancy, and as far as I know, we have not advanced to the equivalent point. But this doesn't mean that there isn't an answer.