It sorta worked for me
I started with my current employer as a phone support goober for $9 an hour, and moved to programming after showing I could do it by dint of an epic 13-hour hacking run to fix something that'd stumped the people working on it for weeks. (It took thirteen hours because I was learning how to PHP in the process. I already knew how to Perl, though, which was a pretty significant advantage as Perl:PHP::Legos:Duplos.)
Actually, come to think about it, if I were to give you a single piece of advice on what to learn, I'd say this: spend some time picking up the basics of a few common languages such as C, Python, PHP, Perl, Java -- not working toward really in-depth knowledge of any of them, so much as giving yourself a broad base on which to build. This'll pay off more if you get a job with it, but I'd argue it's worth doing in any case, for at least a few languages; it's amazing how useful the ability to put together little programs, especially little interpreted programs in a language like Perl or Python, can be in just making a computer more pleasant and straightforward to use. I'd also spend some time getting acquainted with Linux and network administration, if you're interested in going for sysadmin-type jobs; as with the programming languages, it's not so much about getting super in-depth as it is acquiring a basic knowledge of how to get around and do things.
Then, once you've got a survey-level knowledge of some technologies in common use in the fields you're looking to enter, you'll be able to combine the possibilities you listed: you can use the honest approach *and* rattle off a half-dozen languages and platforms in your CV, while also noting that your knowledge of them is at a level that'd make you a good trainee/intern/junior/dogsbody-level worker.
My other advice would be: you're more likely to have success with smaller companies than with bigger ones. Applying to a place with a massive HR department is something like playing DDR on the super-extreme-heart-attack difficulty level; if everything in your CV isn't lined up exactly how they want to see it, it's very likely they'll round-file it and that'll be the end of that. The smaller the company (as long as it seems solvent and likely to remain so, that is), the better your odds of getting a chance to talk to a technically knowledgeable person and getting a chance to show that you have chops enough to be worth hiring -- and consider also, if you aren't able to find anyone looking to take on a trainee, that you might be able to take a support position or similar to get your foot in the door and a chance to show you know what you're doing.
Well, hell, it worked for me, anyway. Here's hoping you find the kind of position you're looking for.