Even without the record I would expect you to have a hard time. I'm surprised you're getting offers. Try to keep in mind that there are people who 1) Have 3+ years experience, 2) Have portfolios, 3) Have references, 4) Have clean records, and 5) Still can't find work. Yes, it happens, believe me. So, you're going to have to get way, way, way back in line behind those people. And that's fair.
In the meantime, just get whatever work you can.