Aiwa CDC-MP32 Headunit Unresponsive

Why 10.4v instead of 12v?

Here's the problem. There is no information on the threshold for the input to the MCU. I'd like to see it up around what you'd get from the 5.1v Zener diode but... The zener is breaking down at a lower-than-expected voltage. I might believe 4.9v but not 3.9v and 3.6v is even more strange.

Your meter seemed to read correctly when you checked the supply voltage for the MCU.
 
It should be easy enough to check one of the new zener diodes out of circuit by attaching it to the lab power supply with a sensible dropper resistor in series (10k or whatever) - cathode towards resistor, anode on power supply (-) out.

Without soldering anything at all, one could also put a finger on the zener in operation... if it stays stone cold, chances are there is something in parallel to it that's drawing too much current. A leaky electrolytic would be a prime candidate, for example...
 
I wouldn't want it to be greater than 5.1v but it should be very close to 5v, especially with the series diode bypassed.

You could also try connecting the 5v regulator supply voltage (confirm that it's at 5v) to that pin through a resistor (1k). If that doesn't bring the input up to 5v, I think the MCU may be defective.