Do a side project, sell yourself on it, unless it works out and you can profit from the side project itself.
My side projects are what swayed them. That and knowing some specifics to media of course. It wasn't solely the side projects, but they helped display a breadth of skill that I otherwise wouldn't have been able to with only work that I was paid by somebody else to do.
In the media company I now work for, my manager is pseudo-technical. He had an engineer sit in on the interview for any technicals. Outside of the side projects, one of the major points I scored with them was that I knew anything at all about Adobe DPS -- and I hardly knew a thing. Vague private interest in how modern publishing was being handled translated into a position in a company that does it. Downloading an outdated demo at one point to play around for an hour or so translated into talking points. The engineer relied more on general technical knowledge for his approval, and seemed to avoid the typical "programmer interview" questions.
So! I guess my point is that people shouldn't rule out play as valid experience! Isn't that how most of us started on this kind of work to begin with?
Do things, build things, break things (and then fix them)!