If you are talking about web-based development, you have to build a complete application all by yourself, from top to bottom in my opinion.
This means all design work, UI, HTML, javascript. All backend application code that serves the the app/endpoints etc including any database components. And finally you have to have configured your own linux box running the aforementioned application components.
This sounds really overwhelming because it is. And I honestly don't think, statistically speaking, the majority of web-devs would be able to pull this off all by themselves. (I'm not talking about HN cuz I'd say the inverse if we just sampled HN web-devs).
The point is that you are going to get your ass handed to you trying to figure it all out and you are going to feel inadequate and scared and maybe want to give up. I don't know, but I think this kind of "test" proves to yourself whether or not you truly care about making web-based software.
The important realization here is that if you prove your passion to yourself I super-guarantee you this same passion will emanate through your bones and you'll have no problem convincing any company to give you a shot - passion is infectious.
Realize that the quality of the application is not as important as the fact that you yourself actually finished the project, it works (to some degree of work) and you can show it off proudly, source-code and all to your potential employer.
You don't need to be a super-designer; I'm not suggesting you train to be an elite systems ops guy. I'm saying show you are not afraid of being a "problem-solver" by solving problems, and you'll be fine =)
Best of luck to you.
