I'm having the exact same problem with my old fridge-that-came-with-the-house. Sears repair guy said it was a broken fan, replaced the fan, fridge worked for a couple weeks and is back to spilling water down inside from the freezer. I think it's time to buy a new fridge!

I'm a little concerned that all the frozen meat in the freezer may have been ruined by thawing a little and refreezing. How would I even know?