If you want to do web design (or graphic design) the field is glutted with the number of 'designers' out there. Pure print graphic design is probably the hardest to find a job in right now, especially if you have no web training. If you want to get into web design, you're very best bet is to learn some programming. Either Javascript, actionscript, flash, PHP, MySQL etc.
Bachelor's degrees in GD will give you a leg up generally. I graduated in '07 with a BA in graphic design and my college internship working at a newspaper art department turned into a full time job. It didn't pay very well but it was a start in the field outside of my freelance work. Then the economy took a down turn, the newspaper laid me and a few other designers off and I spent 6 months trying to get another design job. Had some good promising leads initially but nothing materialized. I did a few side jobs but currently I'm working a sales position.