I got hired as a programmer five years into my career by a senior programmer friend/mentor who joined a start-up company. All I had done before that was help desk and sales support. He knew me pretty well (we were longtime drinking buddies) and knew I had the aptitude for it. The company sucked, but working for/with my friend was a great learning experience and set me on a great path. Thanks to him, I'm making twice as much as I would be if I had stayed on that career path, after I put up with working for a shakey start-up.
Therefore, I suggest "playing golf with the right people" is the way to go. Obviously, if golf is not the thing, figure something else out. Try joining programmer user groups and giving presentations. If you look like you know your stuff, they will trust you even if you don't have the resume to back it up.