Thank you for the additional information. I am sorry to hear of your dilemma. I realize how frustrating this is for you and I hope to provide you information which is accurate and useful, even though it may not be the news you were hoping to get.
While common law allows tenant to terminate a lease if the landlord fails in their maintenance obligations and it renders the premises unhabitable.
While a broken fridge is inconvenient, it does not render the premises unhabitable.
So, your remedy is to sue the landlord for breach of the lease. You can recover any damages you incur for spoiled foods and being forced to eat out, as well as other damages you can connect to the lost appliance.
If your damages do not exceed $5000, you can sue in small claims court. Small claims court is designed to be a "user friendly", simplified process, so that you can present a claim without an attorney. Also, it moves much more quickly than regular court. You can get the necessary forms to start from the clerk of the court.
I am sorry you can not terminate the lease. I wish I could tell you otherwise, but I do not want to see you spinning your wheels on this.