Brand new starter. Good battery. Won't even turn over. What could be wrong?

This link should help:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-selected-other-vehicles-46563-3.html#post235560

Run the tests in the link. It may be a bad ignition switch, in which case you want to check it for wear, pitting, or melting.