I have a BA in biology, and am currently working on my PhD, also in biology. None of my work has anything directly to do with computers. However, as much as I enjoyed learning about science, I've come to understand during my PhD that research is not something which I want to spend the rest of my life doing: I'm not driven sufficiently by it. Instead, I've looked to what I do as a hobby, and am applying for programming jobs.
I have no academic qualifications relating to computers at all - I was massively turned off by "IT" lessons at school, which were in fact "Microsoft Office" lessons - but I do have some summer work experience setting up a database and doing software testing, and I've worked on various small personal projects over the years.
I've been pleasantly surprised at how open companies have been to the prospect of employing me as a programmer, and both companies I've applied to so far have interviewed me. I didn't quite fit with the first company, who seemed rather geared towards mathematicians (one of their earlier hires had a psychology PhD though), but things are going well with the second and I'm very hopeful.
Admittedly, I do have a harder-science background than you (not that biology is really up there with physics/chemistry/maths/engineering in most people's perception) and a PhD-in-progress to catch the eye. But I'd get your CV out there, make sure you mention the languages you know and your open source experience, and do some reading around fundamental CS concepts like computational complexity - you might be surprised. Having practical experience with real-world projects is arguably just as or more valuable as having formal education but never having used it outside of assignments, and being self-taught shows a deep level of interest - you're doing it because you enjoy it, rather than because you saw a paycheck in it. You need to find the right people to see that side, of course; I would in particular see if there are any companies specifically advertising jobs for graduates, since they won't be expecting years of industry experience in the first place.