I wasn't a computer science major, but I did complete a handful of computer science courses in college, and easily aced them all. Then I graduated from college, realized that being a math high school teacher was as close as I ever was going to get to having a job where I got paid to do math (that was my major), and decided instead to pursue a career in programming, which isn't necessary math related, but programming in my opinion is the best next thing.
I did odd IT jobs here and there. I did some multimedia work on a temporary basis. Then got a job working with proprietary technology. Then realized that getting good at proprietary technology wasn't going to take me anywhere, and spent over 6 months attending an IT learning center where I learned ASP.NET development. I applied for web development jobs while taking the course, but I didn't get any job offers, and almost no interviews. The one person who interviewed me sarcastically asked me if I even knew what a type is.
And even if you master all those technologies (which unless you are a savant is going take some time, since some of them are very deep), your work will still be judged on its artistic value (I have little artistic talent), or perhaps on how well you integrate theoretical knowledge of computer science into your projects (I am not a computer science major). And that's if you can persuade the people in charge of hiring to take a look at your work, since, if you are a like me, you probably have no professional experience as a web developer.
At times I wonder if I made a mistake trying to get into this field. As of right now, by the way, I work at an IT company, where I don't get paid to write code but to review code written by other people. If this job is ever going to take me anywhere, I don't know, but it's all I could find.
I wish I could just go to school, complete x number of courses, and be competitive for a web development position. But it's not that easy. Or is it?