Thank you to all of you for offering to share your experiences. So, where I currently am with the car is that the headlight switch replacement resolved the smoking. When I'm home tomorrow I'll send a pic of the old melted unit.
This appears to no longer be an issue.
Once I replaced the switch and reattached the battery I used the key fob and hit the unlock button twice and put the key in the ignition within 30 seconds per the owner's manual instructions on synching a key. I saw the lights blink, but, did not hit the lock button, so, I don't know that the light flashing equates to the button actually controlling the locking mechanisms.
I immediately turned the key and the car started and ran for about a second.
I tried it a second time and nothing happened.
I work out of town so I won't be able to check fuses until tomorrow night, but, I've been advised to check fuses 9, 35, and 37. I'll do that tomorrow.
Is a "hard" reset (disconnecting both battery terminals and touching them together) a real thing? Does it do anything?

Again, I really appreciate the help.