Pontiac Grand Prix starting issues

My 2008 Grand Prix has developed an intermitent starting issue. The car always starts in the morning. On some days after I have driven to work, grocery etc it refuses to start. Dead. No sound, no “click click”. If the car sits for 15 minutes it will then start. The dealership has replaced the relay in the transmission that tells the car what gear it is in, replaced the battery and cables, suggested I try using my husband’s key instead of mine. It still happens. It has done this about 7 times since October. Any suggestions?

Have you tried starting the vehicle in “neutral?”