I've seen this called Technical User, Super User, or Analyst. The way I've seen people progress was to find a position that built on their non-technical skills, working with people of even less technical ability. Then they become the department guru in that product, or at least the laison with the technical people. Once they have a few small projects under their belt (and a couple of courses at a training center or community college in foundation-type courses like Programming 101), they go for entry-level technical jobs. Also possible to do some volunteer work in the product of your choice to create some professional references and/or intern.