Yesterday Chris got an email back from them. They'd finally gotten around to our PS3 and we could come and pick it up. There was nothing wrong with it, really, it had just gotten switched from HDMI to AV output. Haaaakward. Now we look like idiots and we could have been using our console this whole time. Lame. On the plus side, though, they didn't charge us for it at all. What a nice bunch of guys, am I right? If you are in the area and are looking for games and enjoy supporting small businesses as much as I do, be sure to check them out.
But yeah, so, if you found your way here because your PS3 just stopped showing video one day and you're looking for answers, make sure you haven't just accidentally reset the video output mode. Here's a quick and simple video explaining how to switch a PS3 from AV to HDMI (or the other way around, of course):