I don't know if I speak for anyone else, but I've done resume filtering/interviewing in my own company, so I'll tell you my opinion.
Software engineering is a very soft profession. What I mean by that is you can take two people of equal salary and yet one person might generate 10-20 times the value of the other person. The problem is that in our profession it is super easy to stare at the monitor, type away on the keyboard, look completely busy and productive and yet spend a full 8 hour work day not delivering anything useful.
So the biggest challenge for people doing the hiring is identifying individuals who have a passion for being a software engineer. We look for people who have natural curiosity for learning things. Who enjoy building code just like they enjoyed playing with Lego kits when they were kids (or adults, still acceptable). People who care about what they produce and who get intrinsic value of doing good work and delivering solid code.
So how does an interview demonstrate such passion? Well, what's your story? Here's mine: My father bought a book about Basic when I was 9. I didn't have a computer and yet I read that book cover to cover at least 5 times and I "programmed" in a notebook (the paper kind). I learned C++ in 8th grade and x86 assembly in 9th. I knew I wanted to be software engineer 8 years before entering college. Clearly I picked a CS degree. I come home and I code because as a team lead I spend most of my time doing other things. Coding for me is not work, it's relaxation.
So how does that story compare to yours? Do you have a passion or do you simply think computers is a well-paid profession? Even with all the filtering effort of trying to identify good candidates, we still end up with plenty of people who simply want to work, get paid and go home. And that's fine too, but we are a looking for people who will drive our teams forward, who will push for improvements and for better practices.
Having said that, if you have an business degree, I will not dismiss your resume based on that alone. But you need to show me that you truly enjoy the craft. Even with CS students, I still look for any extra work they might do outside of classes. Do you write code at home? Did you post any online? Do you participate in any clubs? Organizations? If you have an business degree (or CS for that matter) but you are simply looking to make money in programming but never cared for it much outside of required learning, I will definitely pass on you. Having CS degree counts for something (even if not much) so in your case, you'll have to work that much harder at proving yourself.
And don't get me wrong, I'm not saying if you weren't programming in diapers you are not hirable. To give you another example, I gave green light to a guy who never touched computers until college after he changed his major from music to computer engineering. But he demonstrated his drive, determination, curiosity and willingness (as well as ability) to learn. That was one of the best decisions I've ever made.
If you are very serious about changing professions, a while back I heard this advice and I thought it was a very good idea: Don't look for a programming job. Find a company you like (good culture, good people, good product, good future...). Continue doing what you studied to do (i.e. business) and get to know some people. Then strike a casual conversation with an engineer (hallway, lunch... no bathrooms though) and tell them you'd like to learn some programming and are willing to help them with their work outside your normal responsibilities/hours. All engineers are always swamped. At a minimum they'll ask you to write some non-production utilities to take care of some annoying issues that have been bugging them. After few of these projects if they see you having value, you might be able to approach management and ask them to be transferred over permanently the engineering team. You will already have some knowledge of team/product and they already know you can deliver so you would be a much lower risk than hiring a stranger from the outside.