Lets double check the grounds first. The negative battery cable has 3 leads coming out of the connector at the battery. One goes to G100 whic is the main engine/starter ground. one goes to G101 which is on the rt fender behind the battery, the main body ground. It will have several wires with it on a stud , make sure all the wires are clean and the connection is tight. The 3rd lead is the clean ground where ALL of the electronic modules are grounded, including the BCM, PCM, antilock controller, air bag controller, digital cluster, FDc, CCP etc etc. Near the battery you should find one large one wire connector, wit a larger gage black wire on the battery side and and equal gage black/white wire on the other side. Make sure that connector is clean and tight. Follow the harness back toward the firewall, in the conduit you should find splice 120, visually inspect that it isn't crawling with corrosion. there are at least 20 ground wires spliced there.
The terminals at the BCM you called out are A12 main ground. C3 door jamb input. c11 not used. c12 accessory(switched)power. I know how hard it is to see those numbers..what color(s) are the wires on the connector side? a12,b12, and c12 all go to the internal voltage regulator in the bcm, as do d13 and d15, and c13 and c15. D13 is the power supply for the VF displays. C13 is 5 volt reference for the FDC and CCP.
I still suspect the ECC power module. It is the only connection where 12 volts could get back to the BCM, via the blower feedback circuit. Inspect that connector for corrosion or being melted.