2003 Grand AM Starting Issue

I have a 2003 Grand AM. Drove to store last night and all was fine. Got back to car and tried to start but nothing happens when turn the key. Radio and lights strong. Battery checks out fine. Just to be sure, I brought it home and charged it all night. Still won't do anything. Tapped on starter while turning the key but nothing happens. No solenoid click when turn key. I have a second 2003 Grand AM so I have done some experimenting. When I put press brake, put car in DRIVE, and turn key on second car, it acts exactly like the car that won't start. When turn key and hold it, both cars turn on lights for a couple of seconds, radio plays, but then all go off. When I put second car back in PARK it starts fine. I tried putting first car in DRIVE and then putting it back into PARK with a little force hoping that I might set a switch or something with the shifter. No luck.

No previous issues with starter.

I used a screwdriver to jump/short the solenoid on the starter. Solenoid spun freely. Starter did not engage but I didn't expect it to. This makes me think that it could be an electrical issue or a safety switch.

Are there any switches or relays that I need to check? I looked at the starter but it is in a place that looks hard to work on. I thought about taking it off and having it tested but I was hoping that you guys might have something easier for me to try first.

Thanks in advance for the help.

I just found the issue. Somehow, the car security system was invoked. I read several other forums and this is a well known issue for this car. Could possibly happen again. I'll have to keep an eye on it.

Solution: Turn key to ON position and let it sit for 10 minutes. The Security light will stop blinking in about 10 minutes. When it stops blinking, turn key off and then start the car as usual.