I knew nothing about web dev 2 years ago and am now a senior sw eng at a successful company. Self taught.

Do everything you can for free, experiment with all at your disposal, and get passionate about the stuff that you don't know that you never think you'll understand. Then find a lower level eng job somewhere with kind smart people, and shadow the hell out of them every day :)

Some of the best developers I know aren't CS majors. If anyone has stigma, it's b/c they either need someone with skills to handle some insane new architecture or data handling at big scale, or they're just misinformed.