|Write a web browser that actually works, sell it cheaply, and retire to Costa Rica at 42.
Seriously, you picked a lousy time to break into a new field, and that's probably more the reason for your lack of success than anything. When people with graduate degrees are happy to find work flipping burgers, a beginner doesn't stand much of a chance. Keep studying, and keep trying; this won't last forever.
In the meantime, I'd suggest creating a portfolio of websites for fictitious companies, displaying different styles, layouts, and functionality, then host them on an inexpensive but professional webhosting provider. Do some checkout carts, membership only features, fancy search stuff - anything that will demonstrate how versatile and competent you are. When you submit an application, include links to your demo sites so that potential employers can see for themselves what great things you can bring to them. I think that might well give you an edge over the competition.
Good luck! I know what it's like to be unemployed for long periods. I spent 12 long years working for minimum wage and few, if any, benefits before I found my current job. And it's by far the best job I've ever had.
"A Journey of a Thousand Rest Stops Begins with a Single Movement"