Sorry my first post is asking for help. I'm not new to car forums, but I don't have much experience with the GP.
2004 Grand Prix, about 67k miles.
Cleaned it up after getting back from my son...including what I considered a careful, low pressure, spray of the engine. Possible cause?? It had no startup issues immediately after or for a couple of days.

Drove it the day before this started with no issues, ran great.
The battery is less than 2 years old.
After not starting, I checked and the battery cables had significant corrosion built up, as they did when I replaced the battery in 2017. I cleaned these up, the connection is good now. No change.
The battery is charged, I've had it on a charger for days.

I do think the battery may have been dead to begin with, even after driving continuously for a good while the day before.
I would think the car would start even if the alternator was bad, if the battery was charged, so I'm temporarily ruling that out.
Starter? Maybe, I hope not. I hear a click, so I assume the solonoid is ok. I could be wrong about that.

I doubt this is a passkey 3 issue, although with the error messages, it does sound like the manual describes when it kicks off. I've been through the service manual routine for resetting the keys. 10 min/5sec/10 min/5 sec/10 min/5 sec from on to off etc. as in the bulletin. No change. Both keys.
Then, randomly, not after this, but later, the car started perfectly. Turned off and then on, testing both keys, it started fine. I did not drive anywhere. Then turned off and it never started again. Power is still there for everything else.
So, I'm thinking intermittent ground issues, maybe something finally broke loose?

I'm open for ideas. At this point I suspect grounding, but I don't know where all of the grounds are to check this.
I have a brief video showing what I"m seeing in case that helps.
I could use help with ground locations to check. Thanks for any help!

https://youtu.be/V5q9BrL_bUw