Q: Honda civic coupe EX, 2004. Locked in park. Car won't turn on. Makes no attempt to turn over.

Recently car had trouble starting because it showed it was in Park and Drive at the same time. Both were lit. Jiggled shifter, showed "drive" only and car started. Shifter has been feeling very stiff and hard to move. I drove car today and shifter felt normal again. Car started fine. Drove fine. Parked in driveway, came back 5 min later and car was locked in park and would not start. No attempt to even turn over. All accessory lights work. Horn and brake lights work. Can hear a little click by shifter when trying to turn on (solonoid?). Have not checked battery connections or fuses......Just went to check if lights dimmed a lot when attempting to turn over, and car surprisingly just started. But it makes me nervous and I want to diagnose. Who knows when car just won't turn on.

My car has 143000 miles.
My car has an automatic transmission.