The people who've said networking is the way to go are, of course, right. All my best jobs have come that way; what few I've gotten from the classifieds (online or otherwise) have been crummy.
But either way, I've learned that it's best to try for jobs with smaller companies. Anyplace big enough to have an HR department will, often as not, screen out your resume if it lacks some credential they specify (college degree at a minimum, usually), whereas a smaller outfit will have a human reading them and might actually give your application enough attention to see that you have something to offer.
Once you get an interview, your degree or lack thereof no longer is important. Just like it won't matter if you actually get the job. What the degree does for you is keep your resume from being tossed out the door during the first round of culling.