Is there any way to escape a terrible cumulative grade average?
Perhaps something to look into are post-baccalaureate programs. I'm not sure about in your country, but in the US there are a handful of post-baccalaureate programs for students in your situation -- students who want to go to graduate school, but haven't performed well enough academically in undergrad to have a good application. The programs vary, but usually consist of a year or two of courses on a particular subject and a certificate is awarded at the end.

A friend of mine wanted to go to medical school, but she went to a very difficult engineering school for her undergrad, and thus had a low GPA and didn't get into any medical schools the first time she applied. So she did a one-year post-baccalaureate medical program, where she excelled academically, and then applied to medical schools again and got accepted.