How to diagnose an electrified refrigerator frame?
An open ground is not in and of itself a problem.  Grounds are there to dump excess voltage in case something goes wrong. If all our appliances worked properly all the time, there'd be no need for ground.

So what you have is two problems:


Your fridge has a bare wire rubbing against the frame or other electrical short,
And, the safety device meant to mitigate such a fault (ground) is broken.


If I were you, I'd replace the outlet, preferably with a GFI, and make sure the ground is attached.  Then I'd have someone in to look at the fridge.