What route?
What country were you denied a visa?
Can you reapply for another visa?

Is the ticket refundable as per ticket rules?
That will answer the question as to whether you are even entitled to a refund before/after departure.
If you dont know the ticket rules, please post the fare basis letter here, or origin and departure, date of purchase, cabin etc.

If you can get a refund, you would need to talk to your 3rd party OTA (Priceline) and not ANA/Operating carrier.
ANA ticket stock booked on 3rd party OTA simply means ANA did not sell you the ticket.
They sold it to Priceline who sold it to you. So you need to deal with Priceline.

Is the ticket changeable/Can you reroute to avoid the country in question?