in addition to some of the useful comments above...
...leave the qualifications to one side for the moment and consider your interests, passion (if you're lucky enough to have one) and preferences for web work.
I've worked at a high-level in media and advertising for 15 years, and with the web for the past 10. A lot has changed, yet there are many career opportunities within the industry. All employers use qualifications to reduce the risk of taking a stranger on-board.
Another way of reducing risk is to choose someone who has proven their ability and is enthusiastic about their work.
So, be that person first and get the qualification in something academic/creative/technical. If at all.
I have a team of web technicians who are all self-taught - many technical staff are. I work with designers who studied fine art and then taught themselves flash + action scripting to bring their designs to life. I know early web-designers who are know focused on usability issues and how to create information architectures. I've had students straight out of college who brought nothing useful from their course.
If you have an interest in web, you now have the option to focus in on what you like specifically. The days of general web design are drifting away.
So, put the courses to one side for a moment, try creating a few of your own sites, try to focus on what you like most about the process and continue it. Then choose a course that gives you an opportunity to develop that area. Oh, and did I mention doing your own sites or collaborating with others....? There are plenty of deserving causes out there that can't afford a site of their own.