I must ask this. What is the length of time between frig openings? It seems to me that if you went into the frig at least once a day, then you would know that there was something afoot and could take action, such as getting some dry ice and an ice chest while awaiting an old frig.
And please do not think that I am defending the old skinflint of a landlord that is giving you old appliances. Check your lease. I seriously doubt that there is language in there that would force him into giving you a new one. And I do not think there is language that makes him responsible for replacing the food.
Jay