Well, if you want a teen film maker's perspective...
With a budget of zero, the first thing I'd try to do is clear out the fridge and even remove a shelf or two if I had to, and then restock the fridge around the camera. Of course, there's still the problem of OPERATING the thing...plus, if it's really all that big that might not work...
If you couldn't do THAT, then I would create a very cheap inside of a refrigerator to go in front of the camera. In theory, it really shouldn't need to be all that intricate, right? Just a few shelves, some food, something to open that looks like a door. You MIGHT not even need the refrigerator itself, just props to go in front of the screen. But then again, lighting isn't my forte, and being inside of something probably changes the way that looks a reasonable amount...
Anyway, I don't know what I'm talking about, but that's the way I'd approach it.