There are plenty of places (at least there are here in the UK) who are willing to take on non-IT grads as long as they show a certain amount of determination to get into the field.
I got a BA in Film and Video ... then went to get my current job as a programmer on such a scheme .. i also interviewed for another such scheme. The Certification will certainly help you if you go for that kind of route to employment. However nothing beats experience ... get yourself involved in something like this
http://www.javaranch.com/ubb/Forum37/HTML/000393.html and then you'll have something tangible to put on your resume
Pounding at a thick stone wall won't move it, sometimes, you need to step back to see the way around.