How much should I know about computers before getting a computer programming degree?

Computer programming and computer networking are different disciplines. You should consider at least trying your hand at both before making a decision. Which major your switching from and what you're most interested in as well as whether you prefer to work with hardware or software are all major things to consider when making this decision.

Do you prefer math and logic, or spending time configuring firewalls or running network cable?

Neither is simple but making an attempt at just getting your feet wet will really give you a lot of insight as to what each of them really consists of.

Unfortunately, your background and interests are unclear... I hope this helps!

In my experience it doesn't matter how much you know going in. What matters is how driven you are to learn more and your natural aptitude to learn better approaches for doing things.

I've met people who have amazing computer knowledge and excellent "book smarts" that can't design and implement a practical system. I've fixed very serious problems in programs that were written by people widely considered to be the "smartest guy I ever met". The reality is that results are what matter. You can achieve results if you are driven enough to focus on getting them and learning what you need to learn to achieve results. The internet can answer most programming or networking questions. Just learn the basics in school and grow from there (on your job)

Also, computers are constantly changing. What you know about computers now will become less and less relevant as technologies change. If you fail to keep up you will also become less relevant. As I said, the most important thing is to be driven to embrace what's new and use it in a practical way. Most of what you learn in college will probably not practically apply to your job. If you aren't learning constantly on the job your job is probably too easy and almost definitely boring.

That being said, there is definitely a market for extensive knowledge in obsolete technologies as well. Very few people know how to troubleshoot a token-passing network or problems with serial modems for example. Both are commonly used in some industries where infrastructure changes at a slow pace (you'd be surprised)

Your comment about linux... You don't need to use linux to be a computer professional. In my industry I have yet to use a mac or a linux box for anything. You will encounter people people in college that will look down at you and consider you stupid because you don't know linux. Every now and then I see one of them from my class working at staples (get my drift?). Results are what matter.

Jacob, Moi is steering you correctly. Application development and programming can be more difficult to get the hang of than networking if your computer knowledge is rather limited. On the other hand, if you are comfortable building websites and the like, then you may wish to try your hand at application development and programming. Speak with your faculty advisor; for the most part, they care about what you have to say. Best of luck.

I kind of thought that a 3 or 4-year computer science degree from a decent university would include both programming and networking and a whole lot besides

You can check the prerequisites for the classes you wish to take. You can learn computer programming or networking directly, without a computer background, if the class is designed for that. You can also learn programming and networking without taking any classes at all, from a book or from the Web—it's cheaper and faster, but it requires that you be good at self-study, and you don't get any pieces of paper for it.

Depends, in many you don't need to know nothing but you should at least know how to use an operative system.

Networking is easier (at least the basics).