Dealer taking no responsibility for fault

We bought a second hand car 2 weeks ago. When my husband brought the car home I went to use the second set of Fob keys. It didn't work. We called the dealer whose response was basically that my husband had signed a document saying the electrics were not covered by warranty. My point was that the key was faulty when it was sold to us so it should be either replaced or repaired. I quoted the sale of goods act relating to items being sold in satisfactory quality but the dealer said it did not apply. He did not point out the defect to my husband when the car was sold. It will cost £100 to get the key fob fixed, yet we spent £7k on the car. Can I have an opinion please on where we stand? Thanks.