electoRF,
*lease bear with me, here.
Does your fridge have a small fan inside of it? If so, where is it? If it does, it's a frost-free and would be in the freezer. If not, then it's not a frost- free. Only the frost-free types would have the condensate dish, bowl, whatever. Probably should have asked that question at first.
And, I'll have to say, haven't seen a fridge like this one before. Kinda shootin' in the dark...
In the 3rd picture, am I right thinking the "box" with the pipes going around it is the freezer? Or do you think the compressor might be in that box?
Can you get a picture of the entire back, bottom of the fridge and the stuff in there? (Lotsa light!)
What you have id'ed as a sponge is insulation, I think. If it's actually a sponge, is it wet?
One last question: when the fridge was moved, was it kept upright, or was it laid on its side?
Wait a minute. The more I look at pic3, the more it looks like a coil within a coil within a coil. In other words, the condenser coil for the fridge. When running, it should be hot. And it looks like there's more space to the left of pic3, which may be where the compressor is (or inside the coil group).
At any rate, if a frost-free, then directly above the coil group (maybe) there would be a hole (maybe with a short tube) where the condensate would drain from the fridge (usually the freezer compartment). Below that would be the area used for evaporation of the condensate (and any other water from inside the box. And, of course, somewhere inside the fridge there would be a drain hole going out.