No, the Ign Sw must be OK. If Fuse #5 has power, it can only have come from the Ign Sw. Turn the key Off and Fuse #5 should go dead.
The only other easy thing I can think of are the numerous Grounds for the ECU. Shown in pic below as G10 and G11. These are located behind the kick panel at the driver's left foot. There is one more behind there, G04, which is not for the ECU. Check that they are tightened and that there is no corrosion.
It's possible that the ECU expects signals from other sensors and that if they don't exist will fail to turn on. But I don't have any info on this and don't know where to look either.
You could do a pin-by-pin comparison between the ECU plug on your other car and this one and maybe spot something missing.
Posted below are the other sections of the ECM connections:
(Total 6 pages)
All the sensors plus the coils and injectors apply battery voltage to pins on the ECU. In addition, on an auto box, the TCM applies more signals to the ECU. Since you checked all the other 12V supply inputs and the Grounds, there must be one of those other inputs which the ECU expects to receive before turning ON.
Make up some probe which will permit testing at the ECU harness plug (plugged in) with Ignition switched On.
Check the Pin #'s on the diagrams and against the other car.