It is not so much "the set-up" that we need info on, but what exactly the symptoms and any other clues to what is happening as there is a hell of a lot of things it could be.

Give us a bit more info on what is happening...

Engine still turning over slowly with jumper leads and engine running in Kia, or is it turning over quicker?
What voltage were you referring to with the 14.6V, is that the Mazda "under charge" from the Kia via jumper leads or "off charge"?
Mazda battery voltage first thing in the morning after being left overnight? (still not convinced about the state of the battery as there has been insufficient evidence to clear it)
12V Power getting to the ECU (at the plug going into the ECU)?
Headlights bright when NOT connected to jumper leads/Kia (battery/earth check)?
Can you hear the fuel pump working?
Right sort of fuel pump? - EFI vs carbie pump would be vastly different working pressures. Carbie pump will NOT provide enough pressure to run an EFI system, and even a mismatched (too small) EFI pump may not have the guts to get the new engines fuel injection working. This may cause the ECU to shut down as a safety precaution.

Try to go about things methodically as there is obviously a very obvious thing that is being overlooked.

Could you get a hold of an OBDII scanner and list the error code numbers (will be in the form of P and a four digit number, P0*** or P1*** where * are digits from 0-9). Just list the numbers as some of the codes are a bit different from the generic OBDII codes in meaning.

"It doesn't work" isn't giving us a lot to work with.....We can't see or hear the issues so you have to be our eyes and ears and be explicitly clear about your descriptions.

"What, where, when, and how". What you measured, where you measured it, when you measured it, and how you measured it (circumstances). ie "12.6 volts measured at the ECU plug with the ignition on", or "engine turning over slowly with jumper leads connected and Kia engine running, voltage at starter 10.5V under load", etc.