Airlines argue over who is responsible, passenger left in middle

First some background. The FTer bought a ticket with Jetstar that included connecting flights on Qantas. Jetstar is a fully owned subsidiary of Qantas. When the FTer went to check in for the Qantas flight, they said it wasn’t ticketed & required purchase of a new ticket. Naturally the FTer wants a refund.

Now to the current discussion. Months pass. Qantas and Jetstar are still passing the buck over who is responsible. Result unhappy customer. What should/could be done next?