I would use ancient instead of elderly. Even though people would know what you're trying to say, the use of the word elderly in that sentence sounds like you're trying to be funny. If that is in fact your intention, then that is a different story.
I agree with what has been said so far with regard to anthropomorphism, but I disagree that 'elderly' and 'ancient' are synonymous when used to describe objects (or people, for that matter). 'Elderly' just means 'old'; 'ancient' connotes great antiquity - perhaps hundreds or thousands of years., although it will be relative to the expected age of the object/subject.
I heard someone once refer (jokingly) to a piece of cheese which had been in his fridge for ages as 'a venerable bit of cheese'.
Thank you all for your comments. I was not clear enough in my question so, sorry about it. This expression 'elderly refrigerator' is used in the translation of 'Kara Kitap' ( the Black Book ). And it doesn't have any hints of humour;
"You are acquainted with the sounds you hear as you wait: a car going over the familiar pavement stones or over the water standing in the gutter, a door being closed somewhere nearby, the motor of an elderly refrigerator, dogs barking in the distance, the foghorn that can be heard all the way from the sea..."
So it's just the translator's choice in this case, in the source text the writer describes the refrigerator with a word equivalent to 'old' in English.