score:6
You will likely run into trouble leaving Australia, since your new passport is not in Australia's system. However, the good news is that (at last check) they can update your passport details at the border if needed, and after this returning is not a problem.
I would suggest trying to contact them again a few times, by phone instead of emailing, and then showing up the airport nice and early if you can't get it sorted. Bringing your old passport if you still have it would also be helpful.
Section 2.2 of this document is the government reference.