The reason you get rejected from places like Mc D's is that they know you will leave as soon as something better comes along. When they say 'over qualified' it isn't because they are bothered about you getting bored or whatever; it is because they will train you up and right from the start you will be looking for other jobs. If you didn't put your degree on your CV you would probably get interviews for them.
OP how can you be a graduate and never had a job? A degree isn't a golden ticket anymore, it is part of the puzzle- employers often want someone with work experience and a good education. Volunteering is the best way to go, and try and get someone to check your applications before you send them off, many good people get sifted out in the initial round because of a poor application.