Alrighty so here's what you could try to do in the sports realm:
1. Apply for internships with various sports franchises of your choosing. Most positions (okay- all of them) don't pay but they certainly do help you get your foot into the door of the sports world, be it the administrative side of things, the marketing side of things, or even the IT side of things (considering how much analytics and number crunching goes on in the modern sports world, there are definitely places in the sports world for people who can keep the computers and technology up and running)
2. Get into writing/talking/pontificating about sports. I know, not exactly a lucrative career (even for the most successful) but if talking about sports is what you love doing, there are certainly ways to make enough money doing it to survive (I mean, Aaron Bruski has a job, doesn't he?). Once again, this is a job that won't exactly pay you to start off with but (and this is a BIG but) if you build up enough of an audience that enjoys what you have to say about Team A, B, and C, or simply likes you as a personality, you can find a role some place or another.
The key here is to polish up your communicating skills: write game threads (my schedule doesn't exactly allow for me to write about every single game at this point- hint hint, nudge nudge), start a podcast (something that someone brought up in a thread a while back), start breaking down game film like Draftexpress, get active on social media. Hell, I don't know if you're based in Sacramento or not, but I've long thought that there's enough of a niche in the sports market in the Central Valley for an exclusively digital sports media site about sports in the region (not just limited to the Kings but Republic F.C., the River Cats, UCD/CSUS, prep sports, your mom's roller derby league, Uncle Larry's Pie Eating Contest, and so on and so forth). Hell, before I moved out to Japan for my job, I was halfway to actually opening a site like that up (being unemployed for half a year left me with A LOT of free time).
The most important thing is that you have something interesting to say. Give people a reason to pay attention to you. Whether its as the smarmy smartass (Dave Dameshek for NFL.com for instance), a straight up news guy (Cowbell Kingdom when they aren't bemoaning the loss of IT), or as an armchair analyst (draft express, for instance. Hell, Mel Kiper started out his NFL draft scouting as a hobby), find your niche and build yourself into the perfect fit for it.
Opportunities do exist. It's simply a matter of putting in the blood, sweat, and tears to take advantage.