Dyson Airwrap Hair Styler Malfunction

Hello, about 3 or 4 years ago, we purchased an Airwrap hair styler. Recently, the product malfunctioned, and we took it to the service center. Unfortunately, we couldn't find the receipt and don't remember where we bought it from. We were willing to pay for the repair service, but initially, they refused to accept it. After lengthy phone calls with the headquarters, they finally opened a variant record and accepted the product for service. After a long wait, the service center informed us that they couldn't proceed with any repairs because the product lacks a serial number. Why did they accept the product for service with a variant record if they knew it didn't have a serial number? Why are they now saying they can't do anything? Did we manufacture this product at home? Should we just throw it away when it breaks down? Is this company, which we thought was so reputable, just a disappointment? I still hope for a solution and goodwill. I simply want to have my malfunctioning product repaired for a fee.