A PNR is a record in the booking system database that holds all the details of the passengers on the itinerary

Each PNR has a record locator ( booking reference), which is several characters ( typically 6 for most airlines ime ) and really needs be quoted when trying to get a refund

When the airline responded to the disputed charge, what was its grounds? you should have been given opportunity by card company to refute the airline's grounds. It should be, from most card companies, quite easy to get a refund for non provision of service