Build a killer resume that focuses on your skills and the tasks you did at each job rather than just "I worked at this place during these dates." Rather than "I folded clothing tables at the mall," write stuff more like "kept store organized and presentable throughout the day."
Stalk craigslist, Indeed, and your local paper, and apply to anything that it sounds like you can do. You might try stuff like, say, being a desk clerk at a hotel... that will give you reception/office management experience and you can then take that and apply to professional office environments. Alternatively factory jobs are pretty frequently hiring, but you may have to get started working third shift and work your way up. But I dunno if that's quite what you mean by "non-retail." Factory jobs kinda suck though the pay is lovely since the job kinda sucks.
Send out a LOT of resumes and applications... and you get lucky.