Can a non refundable registration fee be refunded if the seller backs out of service?

I recently enrolled my two children in a daycare and paid their non-refundable registration fee. This fee was paid after touring the school and explaining my family circumstance. The school said that they would like to have my children and told me to pay the fee so we can move forward in the process. Then four days later the daycare called and said because of my family circumstance they no longer wanted my children in the daycare and that they would not be able to refund the full registration fee.I feel like this money was collected under the false pretense that they were going to be caring for my children only to find out four days later that they do not wish to care for my children.