Thanks everyone for your thoughts and advice.
I went out today and did some looking into the situation. Here's what's I can see that's broken:
1. The 100A Alternator Fuse was blown (there was a gap).
2. The 20A Dome Light Fuse was blown. I replaced it with a 20A fuse. All other fuses were good.
3. The Engine Main Relay has a singed/melted corner.
4. The CDS 30A and FAN 30A fuses are a little cooked on the outside, but the fusible links within were solid.
5. The wiring beneath the junction box is melted but there are no exposed wires right now and it is unknown whether any of the wires are touching/shorted within the mass.
6. The battery cables are damaged, but these too seem to be fine.
I put in a charged battery. It read 12.35v. I took a flat tip screwdriver and pushed the wires such that the gap closed just to check if that would was the problem and if it would turn over. I checked the circuit between the battery - terminal and the 100A Alternator Fuse in the junction box, and it was 12.35v.
Here's what works:
1. The door lights (interestingly, opening the passenger side door turns them on).
2. The dome light.
3. The trunk compartment light.
4. The "key in ignition" bell (when the passenger side door is open).
5. The light around the ignition (the ring of light that helps you find it in the dark).
6. When key set to ON position, the Apexi Super AFC (that I never use) lights up.
7. The headlights and headlight motors.
No headlight intensity drop when key turned to START
No clock, no turn signals, no radio, no mirror controls, no power windows, no lumbar motor, no fan, no windshield wipers. The USB adapter in the lighter port does not light up or indicate voltage.
I swapped ECUs. No change.
I got a reply back from Ty Saxon at TCS Motor Sports. He said that because of the additional labor involved in doing a Celica swap, the base price is $7300. I added up the options I would want and it would be over $10,000, plus the cost to transport the Lorelei to Covington KY from Colorado Springs.
That would pay for a shit ton of labor and parts.
I haven't got a reply back from Nick and NickSpeed, and I don't know that I will. I've also reached out to a Toyota specialist here in Colorado Springs, who seems like they might be up to the task of setting the situation right. They have access to a Toyota tech who was active and skilled in the 80s and 90s.