I received my bachelor's degree in Com S (second major in math) in December 2011. I didn't have the best GPA (I was excellent at programming projects and had a deep understanding of CS concepts, but school is generally not the best format for displaying my strengths), and my only internship was with a now-defunct startup. After graduation I applied for several jobs, had a fair number of interviews, but never got hired. After a while, I got somewhat discouraged, and though I still said I was looking, and occasionally applied for something, my pace slowed down considerably. I remain convinced that software development is the right path for me, and that I could make a real contribution to someones work force, but I'm at a loss as to how I can convince anyone of this. My major problems are as follows.

1. Lack of professional experience-- a problem for every entry-level programmer, I suppose, but everyone seems to want someone with a couple of years under their belt.
2. Rustiness-- I've not really done any programming in about a year, and since school all I've really done is various programming competitions and puzzles. (codechef, hackerrank, etc.) I need a way to sharpen my skills.
3. Long term unemployment-- while I had a basic fast-food job after I graduated, I've been truly unemployed for about a year now. Furthermore, no one has ever hired me as a programmer, and any potential employer is liable to wonder why.
4. Old References-- my references are all college professors and one supervisor from my internship, none of whom I've had any contact with since I graduated.
5. Confidence-- I have no doubt that I could be a good professional programmer, and make just about any employer glad that they hired me, but I'm aware of my red flags as a candidate, and have a hard time heading confidently into an interview.

How can I overcome these problems and keep my career from being over before it starts?