I say you should go for it. I don't think that the recruiter thing is the best way to go, though. As you have experienced, recruiters generally have their hands tied as far as what they can present to potential employers because of experience and degree requirements. That said, look locally. I grew up in a tiny dying town with almost no jobs in IT, but there was a local IT business (WISP, consulting, PC repair) that I got to work for as a helpdesk tech my Senior year in high school. When I went to college, I left on good terms so I had a Summer job waiting for me. Throughout college, I worked there and for the school of Engineering's network helpdesk. When I graduated, I was able to go on with a degree and experience to get the job that I wanted and now I'm working as a network security engineer and I'm 5-10 years younger than all my colleagues.
The point is, maybe don't look for an official start to your career right now. Instead, look for work locally that will get your foot in the door and give you experience. Find a local IT consulting or web design house and ask to work for them. Sell yourself like you did in this submission. If that doesn't work out, talk to your university. I don't know what they have going on, but I'm sure there are plenty of opportunities for undergrads to get involved. Talk to the helpdesk for your particular school within the university (like ECN at Purdue); talk to the university's global helpdesk (like ITaP at Purdue); talk to your professors. If none of those turn up anything (which I find highly doubtful), look into contributing to open source projects. Drupal, Joomla, and friends are possible projects to start with. Just don't quit looking for opportunities wherever they happen to appear and remember that there are more local opportunities than you may realize.