I’m a senior software engineer, and I’ve been involved in the hiring of several web developers. I also have an unusual academic background (a bachelors in English Literature). So let me give you my perspective.
A master’s degree in geochemistry is not worth a computer science degree. But it is not worth nothing, and is obviously more valuable than a non-comsci bachelors.
Your masters tells me that you are intelligent, analytical, can research problems independently and have a good work ethic. This is good; software engineering is a research role that sometimes requires enormous reserves of patience.
However, I also need candidates to possess at least what I’d call the “core” technical knowledge for their role. This is nonnegotiable. I cannot spend two years training you how computers work.
The good news is, you don’t have to learn these skills at university. Many developers are self taught; in fact some of the best programmers I know don’t even have degrees. But you will need some way to prove your skills. As your friend says, the best way to do this is to build a portfolio of work. Personal projects are useful; another approach is to find a para-technical job like QA testing and use it as a springboard into the industry.
A bigger issue may be you dropping out of computer science at undergrad. Prepare a good explanation for this: “it wasn’t right for me” won’t be enough. If I’m taking a gamble on someone with a non traditional background I need solid evidence that you’re committed to this path. What if you finally become a programmer and then a year in decide it “isn’t for you” again?
At this stage, I would spend a few months building more personal projects, and trying to find a role as a tester or another non-programming role in a tech company. You never know: there might be other jobs in tech that inspire you, like QA, systems administration or UX design.
Finally, a word of warning: it can be difficult even for computer science graduates to acquire junior developer roles right now. In the UK at least, comsci grads have the highest unemployment rate after six months of all university subjects. You can certainly do this - I did - but it took time, effort and several rejections. So prepare yourself for a long-haul.