Yes, I tried that method you mention, but no luck. No combo of lock/unlock works to get the start button to activate. Any other way to check what you refer to instead of physically accessing?

Do you have any friends or family that has a bluetooth OBD scanner, and you can download an app like Car Scanner on your phone? Shows codes that don't trigger check engine lights. I've had codes related to my immobilizer and starting system which is how I learned about what I mentioned earlier (drinks spilling near the gear shifter). You can maybe buy a cheap one on amazon. Example I quickly found:

You can’t read the codes without turning ignition on.

Oh right, how could I forget .

There is definitely either something chewed from the rodents (90%), or just some moisture damage to some connectors. I can try and see which connectors are related to the ignition switch, I'm not sure if you're able or willing to mess around with them, or if you have stuff to measure voltages

The dashboard, you said the door open notification comes on. Can you get other things to come on? Like if you turn your headlights on?

I notice that when I am in the car with the fob, the security lights still blinks even after pushing the start button. I also noticed that the start button does light up after pushing the unlock button a couple times, but the LED light doesn't light up. I took out the glove box (where the nest was) and the wires all look good going to those modules. I pulled the bolted fuse links again to make sure- they are not blown. You may be correct about moisture around the connectors- I noticed rust around the glove box screws and various areas behind the dash, and when I first got the car home, the rear footwell was filled with water. I'm thinking there is a sunroof leak into the car, but can't check until I get power back.
The door open notification light comes on, but there is no chime noise. The fob chirps when I lock and unlock.
I would appreciate it if you could let me know which connectors for the ignition; I have a voltage tester.
The following work: headlights, flashers, seat adjustments, cabin lights.
Thanks again.

Did you try again to press the power button with the key fob?

Yes, both with the fob battery in, and with it out. With the battery out and putting the fob against the start button, the dash message says to depress the brake pedal and push start, but nothing happens. With the fob battery in, nothing at all happens.

The best is to get a scanner they are not expensive anymore from Amazon and hook it up to the diagnostic port and run the scan. It is worth having a diagnostic scanner, not the blue driver type but a proper scanner they run around 200 and can help for other cars too. You can also try disconnecting the battery terminals and reconnecting them if you have not tried it already.

Thanks everyone; nothing has worked so off I’ll tow to Lexus soon. I’ll let you know what they say the issue is

Hey larry, before you do that, maybe take a look at this doc with the measurements. I attached it as a PDF. Though if you don't feel comfortable testing it is understandable. Report back

This is great, thank you! You've given me hope.

Would you be able to share ST-17 and DL-121 parts as well?

Sure, I've attached them and extra(s)

Well, after removing the fuse box and bolted fuse to double check the issue, upon putting everything back , now I have no power anywhere. No lights, no fob use, no interior lights- a big nada! There are 12.2 volts going to the bolt on the fuse box holding the large fuse in; alternator is getting 12.2, the ground is working. Am2 is fine, no fuses are blown. Any idea what I’m missing?

Check the main fuse.
Also, check the fuse link, the contacts inside can break.