All electrical goods should be expected to work for a minimum period of 6 years. If a machine fails due to an 'inherent fault' (i.e. poor quality components or poor manufacturing standards) the retailer is obliged to put matters right. (The retailer can choose whether offer a repair or provide a replacement).
For the first 6 months after purchase, any problem which develops is automatically assumed to be due to an 'inherent fault'. After 6 months, it's up to the customer to establish that, on the balance of probabilities, this is the most likely cause.
Get the independent engineer to sign a report stating that, in his professional opinion, the most likely cause of the problem is either poor quality components or inadequate quality control at the manufacturing stage. (He'll probably charge you for the report but it will be cheaper than paying for a repair). Then go back to the retailer and demand that the matter is put right at the retailer's expense. The lack of a receipt does not affect your rights in any way.
Chris