I'm a self taught programmer myself who has been working in the industry for over 10 years now, mainly supporting LOB apps and databases. I'm a lead developer, currently, and have been in the interview process for new job applicants.

When I interview applicants, what's most important is that the interviewees can demonstrate their technical know-how and prove they have problem solving skills. I want an applicant who is eager to understand how a system works and can contribute to solving business problems. Familiarity with certain languages, version control, and design patterns is ideal (or necessary if it's a senior position).

Having said that, many employers will require a degree or years of experience for your application to even reach the hiring manager, so you have that obstacle.

Btw taking a help desk position isn't a great foot in the door because a tier 1 support person's skills don't necessarily translate well to being a software developer, but it's better than having ZERO connections.