Be an intern and work for free until you can build a strong resume that will highlight your automotive skills. Working at a parts store doesn't tell a shop that you are qualified to be working on cars. If the parts store has any training programs that are significant to the career you seek, then include that and the certifications you have received.
I don't know how UTI does it either but most, if not all, shops/independent shops/dealer service centers would want to see the certificate that shows you know what you're doing. And there are a loooot of different certs you can get.
As mentioned above, your chances of getting in also would increase if you already have someone on the inside. I find this to be the best bet.
Also, when you're in an interview and they say the god-awful excuse "you just don't have enough experience," hit them with "How can I ever expect to get professional experience, if no one gives me the opportunity?". They really can't counter that except with doing an internship. Shops cannot afford to pay someone that they feel are not seasoned enough to work on their customers cars.
Ask them for a suggestion to where they recommend you would get hired for experience, I.E. the whole interning thing also. They may know a lot of other alternatives you may be interested in. And never tell them you want to get your foot in the door. That tells them you're too desperate, to the point where they know you would accept minimum wage doing toilet duty. I hope that helps. And best of luck!
