Update:
It's now 10:28PM CST. It's been running on electricity since about 4:30-5pm today. I just checked freezer. For the first time since this whole episode started, I have a cold freezer. I just moved the thermostat inside the fridge portion down about 1 hour ago to about midway, and the fridge is cold! There is even a bit of frost formed on the fins!
I'm letting it run all night, but if this works, I really would like to know why, when I replaced the element the first time, none of this was working properly? Could just simply cleaning off some electrical terminals on the back panel have done it?