Extremely poor service @home and Dyson

I purchased a Dyson vacuum from @home in June 2023 it stopped working in January 2024 and I took back to the store. Unfortunately I do not have the original receipt but I have the proof of payment to @home done. Both Dyson and @home refuse to pay for the repair as I don’t have the original receipt. Surely Syson and @home should have the serial Numbers of the stock they had and be able to match to mine?