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You will need to be sure that the AC is fully "defrosted". Once ice gets into these everything can go bad.
I sorry that I'm going to have to give you the reality of this situation.
If the unit is completely deiced, then you may have broken the sealed system which means that the repair will be more money and/or not feasible. The ice expands everywhere and can crack or pull the system apart. Once that happens the coolant is gone. This is not a DIY type repair.
You can try to unplug for 15 minutes it to see if there's an electronic problem that might reset. This is not too likely though.
Most ACs today are less expensive to replace than to repair. If it's an older one the new one will save you electricity.
If your AC is a newer one and a larger BTU model it may be worth having it repaired. If it's a 5,000 to 10,000 BTU it's probably not worth having it repaired.
I'm sorry I have dealth with mostly smaller units. I don't have a lot of experience with central air systems. I will have to opt out so that another expert with this experience can answer this for you.