I'll chime in here as a programmer with friends in IT: The people who say that you need connections or a degree to get into anything major are right, but mostly because even with that criteria in place there are still tons of worthless resumes flying around, and so the concern is more about cutting down the number of people that you need to deal with than it is about worrying that some qualified people might be being excluded. Tough, but that's how it seems to be.
There are two real ways to get around that filtering, as far as I can tell:
1) Go get a 4-year degree. If you're looking for only programming/computer/IT classes, you'll be disappointed. If you look at it as a time to try out a scattering of new things (Ever taken a course on existentialism before? Management? Now's your chance!) and learn how to learn, that can be a very productive two years (assuming you can transfer over the credit from the 2-year degree). Many four year programs also have connections into intern programs, which is a good place to start getting your foot in the door at larger places.
2) Don't go for the big places that are deluged with everyone who can figure out how to throw together a resume. Look for startups, small companies, things like that and try your luck there. You'll likely have to ask around a bunch, but jobs do exist there, and they generally have the time to actually bring you in and see if you know what you're doing. After getting a bit of experience there, you can move up to work somewhere larger and more well-known.. If you even want to. Many of the people that I know in that kind of role love the job satisfaction that comes with it, and have no desire to move on to other employment.