My 2006 Hyundai Sonata V6 will not turn over. Battery is new, starter checks out fine. When key is turned to start, lights come on dash, don't dim, accessories work, but won't turn over. No clicking, no sound. After car sits about an hour, turns right over. Any ideas out there? This happens intermittingly.

Check/replace the ignition switch for wear and pitting. There's likely an issue here. Check for any TSBs.