My advice is to do whatever the hell you want. Plain and simple.
As for some suggested tactics to getting into programming as a profession, I have a few. But first, you must know that this is based on one premise -- you are actually good at programming. If you aren't, it doesn't matter what degree you have or what job you gain entry to, it will all collapse when, ultimately, you can't do the job and people learn you just can't cut it.
But if you work at it and you honestly learn what you need to know, then getting a job is easy, but keeping it won't be... because you will quickly be promoted out of it.
Anybody can change their career path drastically. For example I have done so at least a half dozen times. Here is how. Just do it.
What do I mean by that? Let's take programming as an example. Just code. Code your own stuff. Join open source projects and be an active committer. But chose you projects wisely. Don't work on projects that aren't directly related to the targeted area of programming that you want to be a part of. If you want to work at banks, then pick financial projects. If you want to work on large enterprise applications, then work on projects that deal with multiple concurrent transactions spread out among a cluster of servers. Make sure you work with SOA if you want to work on B2B commerce.
Meanwhile, participate. Pick out people in the community you wish to join that you would like to emulate, and emulate them. And, most importantly, interact with them. Post comments on their blog that are relevant to the work they, and you, are doing. Email them directly with you commentary and opinions on the industry. Ask them for advice when architecting a new project. Join forums and post helpful answers to newbies questions.
Why? Because there is no barrier to entry to these worlds other than talent. No gatekeeper other than the peers you are asking to work alongside. If you gain their acceptance, a job interview will only be a formality at that point. I know, I have done it several times, and know many others who have done it the same way.
So, do you have what it takes? I doubt even you know at this point. But you must decide to devote yourself to it 100% and spend as little time and energy on what it takes to survive at a bare minimum. Take a job that takes up the least amount of your time but pays enough to keep you housed, fed, clothed, and able to stay connected to the internet. Then spend every bit of your time working at your goal (to include taking time to recharge you batteries and sharpen your saw). One day it will become obvious to you that you just aren't going to make it or you will look around and realize that you are already a part, a participating member of a small core, of the community you desired to enter. Then you can walk into any job interview and get the job, even if you don't have some fancy degree. You will have a reputation and a portfolio of completed successful real world applications and a solid base of experience - not to mention a ton of honestly written gloriously praising letters of recommendation.
Sure, it may take you a little longer than it would have 30, 20, or even 10 years ago, but you still can do it.