So..
1) CV64 works with your other Amigas
2) PSU is working fine in both 4000Ts (PSU checked & switching them with other A4kT doesn't help)
3) Software installation is not the problem (clean install tried, switching working environments between A4kTs (and with modifications instructed in that other thread with A4kD) doesn't help)
4) 12V line is missing in the suspicious A4kT mb (can be found in other one and in A4kD)
If you've tried it all, maybe it is then "simply" hw-problem with the motherboard (with 12V-line or other), somewhere between PSU-connector and zorro/serial.
Hopefully Amiga Repair France or amiga.serveftp.net can help - maybe you could email them about the symptoms&findings thus far and the possibility of fixing?
EDIT: you should try cleaning and re-seating everything on the mb as framiga suggested - this has helped me numerous times.
