Just call NZ.

Tell them you can't access your booking and provide them with the SQ PNR. They'll immediately realise that what you've provided them isn't valid as all NZ PNR's end with a H.

You'll need to provide them with flight details (number/dates), Passenger names and the method of purchase they'll then provide the NZ PNR which can be used to select seats online.

As a Star Gold you're entitled to Frequent Flyer seating (more legroom and/or closer to the door) on Air New Zealand.