Ask HN: How do I get a coding job as a recent grad with a non-CS degree?

I have experience coding, and by all accounts I seem to be pretty good at it. I have experience (even startup experience) but not as much as someone who has been in the Valley for a few years. I pick up new things quickly and can stay focused on a problem for hours and even days. The problem is that a lot of this isn't especially impressive to put on a resume.

I'll be moving to San Francisco before the end of the month and I need a job so that I can pay rent but I'm having trouble convincing companies that I'm a good hire. Most seem to look at my resume and write me off right away.

tl;dr: How can I prove that I'm worth hiring?