It was built 2-3 years ago, roughly. I tried what you said, was able to take off both side panels, but no luck. Unless the thing is overheating instantly, I don't think it could be that. Maybe the first time it happened it overheated, and now it's just messed up somehow? Anyway, after fiddling around some, I think the fans that are mainly going wild are the ones on the bottom of that black box in the middle, which I suspect is the graphics card? I have no idea how to tell which parts are which if they aren't in a box that says so, but that thing is connected to where the video output cable is, so that's my guess. There are two fans underneath it (and for informational purposes, two more fans on the top of the box I had no idea existed). It's hard to figure out which fans, if not all, are the ones going haywire, but I think it might be those.
Could it be the graphics card overheated? I suppose that might explain why there's no picture and wacky fans.