I'm going to go into this with one disclaimer that everyone needs to face. The economy sucks, especially for new graduates with no practical experience. Things being what they are, it's simply not the best time to be looking for work. For anyone. That said, if it's a field that interests you, I can provide my 20 years of experience in the "computer" field in the hopes that you find the information useful, or even inspiring if you're feeling as hopeless as you sound. If the field (programming, sysadmin, etc) does not appeal to you, well, maybe just the inspiration then.
I have no college education. In fact, I'm a HS dropout with a GED. Everything beyond that level is self taught. I make very good money though, and have for most of my life. The easy hiring during the dot-com boom made up for my lack of initial experience and formal education, and eventually experience made up for the lack of all of that.
In this field in particular, almost every degree is useless from a practical standpoint. This is a benefit to you, the new job seeker, because you aren't starting from a worse position in any IT job when compared to someone with a CS degree -- many people think this is mandatory or that it will help. The first one is bogus no matter what the job description says -- I've had jobs with *insane* paper requirements that were disregarded simply because my development skills and personality were a better fit than the guy with the degree(s) they interviewed before me. If your non-IT degree is not directly related to the business, then all it tells us (your potential employer) is that you have an amount of stamina and focus. It's worth something vs. a dropout like me, but not as an indicator of knowledge or skill.
If you are moderately computer savvy, then breaking into the field in a seemingly unrelated entry level position is easier than you probably think; IT departments do a lot of internal cross hiring and promotions, and experienced people can perform any role in the department at a basic level of competence. Long gone are the days when you had a group of programmers, a group of admins, a group of DBAs, and so on. That model has been dying for a while, and although there are some monolithic holdouts, for the most part it's a dead system.
This means that you (yes, YOU!) can probably get a job very easily in the IT department, or a department related to it, and then work your way "over and up" to what you really want to do -- once you figure it out. Which is another beauty of the field. You get exposed to so much as you work that you can dabble in a lot of different things, and pursue the ones that are the most interesting. The first place to look are support departments, be that telephone support for software or desktop support for the non-technical staff (read: sales and management people). These jobs are usually annoying, but require no expert skill level, and the pay is not horrible.
From there you'll be exposed to a lot of different technologies and have plenty of opportunities to learn and grow your skills -- if you seize on them! If you find yourself visiting the same guys computer every day to fix the same problem, you find a way to prevent the problem -- or to fix it remotely. Tada, new skills. If you overhear one of them complaining that they wish _______, you look into what you can do to make it happen. If everything is running smoothly you'll find yourself with plenty of time to do things like watch youtube videos and post on them thar internet forums -- don't do it! Use that time to find and solve other problems. Not because you're gunning for worker of the month and a worthless plaque, but because for most of us in this field, we only really learn new things when we're solving problems. Real problems.
After a year or two in that sort of environment, you should have developed the skills required to do at least one other job at a basic to intermediate level of competency, and then it's time to decide if you're happy where you are, or if you want to change departments (or even companies). The first year is the hardest. It's difficult to break into the field through the front door, and you'll spend a lot of time doing busy work that you think is stupid, and dealing with stupid requests. At all costs resist the urge to look either annoyed or complacent. Don't huff and puff that Bob has asked you to refill the paper in his printer 50 times if that's your job, or that Brenda can't keep the viruses off her computer. Do the jobs with a smile, and LEARN while you're at it.
Network, network, network! The face to face kind and the linkedin kind, not the facebook or ethernet kind. Develop contacts. Make friends. Find people who can teach you stuff, and whom you can impress with how quickly you pick up what they're throwing down.
I started out doing exactly this kind of stuff, and today, I consider myself very successful and am proud of that success. It was easier to break in when I started than it is today, but believe me, it's not impossible. We just fired a guy a few weeks ago because he just "couldn't cut it". Not because what we were asking him to do was hard, but it just wasn't sinking in, and he was unable to solve problems on his own or follow instructions unless they were laid out explicitly step by step -- it takes longer to write the instructions down than for me to do them, so if he's not figuring things out on his own after a while, it's not going to work out.
Hope this wasn't too long, and hope it was somewhat useful. If it was too short, believe me, I can expound. ;)