Prius (Gen 2) :: Key Is In Ignition - Flashing Red Key Symbol Showing Keyless Start

I have a 2007 Prius, package 6. It's always worked great, can't complain. I bought it in 2009 with 27,000 miles on it from the original owner.

I have always started the car by pressing the start button with my foot on the gas pedal. My key fob is in my pocket, I don't put it in the ignition key slot. I lock the car by pushing the button in the door handle from the outside. I unlock it by putting my hand on the door handle and pulling on it. My keys are always in my front pocket with nothing else in the pocket.

Yesterday, when I got in the car and pushed the ignition button, I got the symbol of a red key flashing with a line through it, seeming to be telling me I was trying to start the car without the key. I got my key out of my pocket and waved it around, and then the car started in the normal way, by pushing the ignition button, i put my keys back in my pocket. Went out, came back, everything seemed normal.

Today when I got in the car and pushed the ignition button, got the flashing red key symbol (and beeping sound) again. I got my keys out of my pocket and waved them in front of the dashboard but it was no dice. The car would not start. I put the fob in the ignition slot and the car then started. I went to my location, turned the car off, tried to turn it back on without the key in it but it still had the flashing beeping key picture on the otherwise dark dashboard. I tried to lock the car by pushing on the door handle button but there was no response. I opened the door and used the button on the inside of the door to lock the car and closed the door. i used the valet key, taking it out of the fob and using it to reopen the door. Pushing on the lock/unlock buttons on the fob had no effect.

When I got home, the car still would not respond wirelessly to the key fob. I got my spare key fob from the house and tried using it to start the car wirelessly. It had no effect.

I searched this forum and read about the button under the steering wheel. I went back to the car to search for the button. I saw the button, labeled with the word 'Key.' But before touching it, i tried starting the car keyless again, pushing the ignition button. It started normally. Everything worked normally, lock/unlock, ignition. Key fob not inserted into the slot. I decided not to do anything with the under steering wheel button.

I would like to ask whether this sounds like there is nothing wrong with the key fobs but there is some problem with the car internally.

Are there ways I can test that, by trying other things that would be affected by the battery, if the symptom comes back again? If there's an internal defect causing the problem rather than problem with the fob/s, would any of the causes be warranty repairs?

The car currently has about 67,000 miles on it.