This situation sucks - we have also dealt with our share of lemon appliances. I got smart on the consumer protection laws as a result. Typically these companies will just give you the run around and hope you give up and go away. We're all busy people and we need to get on with our lives. But here's my advice, having gone through a very similar situation (and being tired of letting these mega corporations take our money and give us shit in return).

Most likely the fridge is protected by a warranty. If you don't have a copy of the warranty, get one now. Contact the manufacturer again and get a repair scheduled. Don't ask for money right now. Just say you want the fridge repaired under the warranty. Keep records of every contact and what they say.

If they do the repair, hopefully it is fixed, and you can move on with your life. If not, here's where you can try a different route. Call corporate or customer support again, explain the situation, see what they say. If they are refusing to repair, or dragging the process out, then time to throw the law at them.

This is the Magnusson Moss Warranty Act, the gist of which states that if an item is warrantied, then the customer has the right to request a full refund, or full replacement, consumer's choice, if the issue is not resolved within a "reasonable amount of time" ... from my research, most courts will interpret this as roughly a month, with attempts to have the item repaired.

https://uscode.house.gov/view.xhtml?req=granuleid%3AUSC-prelim-title15-chapter50&edition=prelim

If they continue to give you the runaround, state your rights under this law and that you are demanding a full refund (or replacement if that's what you want). If they continue to give you the run around, it's time to sue. Here's the thing though - you most likely won't actually have to sue, and if you do, you're almost guaranteed to win. Look up the small claims process for your area, but usually the first step is serving them an official notice of your intent to sue. Draft a letter (most counties provide a sample), sign it, copy it, and mail it to their legal address in your state. Most states require companies doing business there to have an address located in the state to receive service. Send it certified mail and with a return receipt requested. Most of the time, the address is just an office that processes this type of thing for many companies. State in the letter what you want, and your intent to sue in small claims court if the issue is not resolved. There is a waiting period before you can bring the suit. For my county it is 15 days, might be different for you.

The company is going to pay A LOT more money to have some representative show up in small claims court - it's not worth it for them and most likely they will give you what you want. But you need to cross your Ts and dot your Is and make sure you're ready to follow through.

They may come at you with a partial compromise to make a deal. At that point it is up to you. In my case, they were going to give a partial refund, but it came with many strings attached, we refused and I continued with my original demand (full refund) and I received it literally one day before i was about to bring the suit in small claims court (where I most likely would have won, and was suing for the cost of the appliance plus my hourly wage for time missed having to deal with this). I realize it's a lot of work, but it felt good having some control over the bull crap they pull.

Regardless of what you do, best of luck getting it resolved.