So there are two issues, 1) companies are looking for more experience, and 2) there isn't much available work.
That suggests to me that there is some work, but that you have to be very good in order to get it. All of that seems to indicate that a strong portfolio is what you need. I would also consider broadening your scope, many web companies are also multimedia companies and often do E-Learning type work.
Perhaps you could do a more multimedia specific course, with the aim of building up a strong protfolio. At the same time identify your target companies (both E-Learning and Multimedia) and see what kind of work they are producing and focus your portfolio on that type of work.
I would also say the creative industry can be hard to break into and its not the easiest to make a living at.