My wife purchased a vacuum cleaner a number of years ago, and when using it it suddenly burst into flames causing burns. We don’t have any receipt showing the proof of purchase, do we still have a case if we could show the product was defective?

There are some tricky issues, but proof of actual purchase such as a receipt is not mandatory as long as corroborating evidence can show when the machine was purchased.  Remember, as long as we know what company manufactured the vacuum we’ve identified the manufacturer, but it is required to know which business sold it in order to sue the retailer as well.