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I am sorry to hear this;
if a company sells a defective product, they are liable for the cost of that product under a breach of contract theory.
A breach of contract occurs when one party did not deliver a product as set forth in the contract; in a sales transaction, there are implied warranties, such as the implied warranty of merchantability; the product is expected to work in a manner in which a reasonable consumer would expect it to work-ie a battery will charge a car; if it does not then the implied warranty is breached.
New york's small claims information is here:
It will be helpful to be able to prove that the issue was not with the vehicle -ie that a replacement battery was used and the car worked fine with it.
checking in on the above; thanks for using Just Answer!