Ok, here's my life story from the last 3 years. I had no programming experience whatsoever when I started.
I start a 2-3 year Master's project (general-ish biology) that involved doing a significant amount of RNA sequencing. I say to my PI, "oh hey, maybe I can save us some money and analyze the data myself". Famous last words. I teach myself bash scripting and R. Data gets analyzed.
To help out other members of my research group, I learn MATLAB and make some analysis algorithms for videos/microscopy data. I write an R package that does end-to-end analysis for some obscure scientific equipment. At this point, I'm having more fun programming than I am with my Master's (perverse, I know). I teach myself Java and start dabbling with video games for PC and Android. I start teaching R workshops at my university's R user's group. I start applying for jobs, finish my thesis, and graduate a few months later. Learn Python.
Get two job interviews after ~10 applications: one with a biotech company and another with a supercomputing consortium. Absolutely bomb the biotech company interview- they didn't mention what technology platform they used... I told them I'm great at sequencing and that "microarrays are a dead technology" (turns out they were a microarray company... lol). Get the supercomputing job.
Reasons for getting hired:
So there you go... that's how I went from "what is computer?" to supercomputing consortium staff in 3 years.