Start a startup. It doesn't matter if it succeeds or fails.
Seriously. While I was in college, I started one of my own -- a development shop. We got one contract, executed it nicely and got some good scratch with which to buy booze and pay a few months of rent. Then we realized that you can't really run a company and do your homework at the same time, and the company fell apart.
I then worked as a sysadmin / tech-support for a little over a year to pay the bills (sounds similar to your situation), before deciding that I couldn't handle doing something I hated any more.
That's when I joined another startup as the lead developer. It seemed like it was going well, then we launched one day after what turned out was a major competitor that kind of blindsided us (Google Groups). After flailing around for a while (and writing a whole lot more software for the company that they didn't feel like releasing), the company was in its death throes and I left.
This was about three months after I'd graduated, and it was remarkably easy to get a job. All the recruiters and interviewers I talked to were very impressed by the company I'd started, less impressed by the startup I'd joined, and not at all impressed by the sysadmin job or the programming job I'd had in high school.
So if you have a few months of living expenses saved up, quit your job and start a startup company. 99% chance it'll fail, but it seems to me that afterwards you'll have a much better chance at getting a job.
What do you have to lose? With two years of tech support experience you'll have no trouble getting another tech support job.