The Background
I have a bachelor's degree in computer programming and information systems. During school I worked as an intern doing network administration and hardware maintenance for a government organization. After graduating, I was hired permanently at that job and I continue to work there. My supervisors knew that I wanted to be a programmer, but they recommended that I take the job offer anyway. They reasoned that it's easier to apply for positions from within the organization than to apply from the outside. Now that I'm established in the organization, I'd like to begin to apply for programming jobs.
The Problem
I'd like to get a position as a programmer within the same organization, but my current job is not programming related; therefore, my résumé lacks in programming related experience. In my spare time at work my supervisors let me program small tools and medium sized applications to help us in our work, but it's by no means a professional programming environment.
If I write my résumé including the work that I actually do ninety percent of the time, then it won't include any programming experience. If I leave what I actually do out of my résumé and only include the (unofficial) programming I've done at work, then I'd really be lying about what I'm paid to do. It's also obvious from the title of my job that I'm not currently a programmer.
I don't have much programming experience outside of work either. I have the work I've done in school which is mildly impressive. I have some small projects I've worked on at home that are mostly puzzle type programs, such as finding prime numbers, converting binary to decimal, the knight's tour, etc. I continue to study and practice as if I'm still in school. I read books on programming and analysis and design, and write small programs to test what I've learned, but I don't have any significant professional programming experience that I can list on a résumé.
I know I have the necessary knowledge and ability to get an entry level programming job. I just don't know how to show it on a résumé, because a résumé typically shows only your professional history.
I appreciate any advice on how to handle this.