Q2 on the RF board is a P-channel MOSFET functioning as a power switch. You can probe it in place. The source (pins 1, 2, 3) are connected to the 12 VDC main power input through a polyswitch (resettable fuse) and a Schottky diode. Verify that you have 12 V on Pins 1-3. Pin 4 is the gate of Q2. When it is grounded, the MOSFET turns on and 12 V should appear on the drain (pin 5-8).
The signal that grounds the gate of Q2 comes from the front panel PCB. It might be hard to probe Pin 4 directly, but you can put your probe on any of the components connected to pin 4 -- R76, R77, or C226.
If Pin 4 doesn't go to ground when you turn on the radio, you'll have to go back further to the front panel PCB. On that board, there is a signal called /PWRON that is driven by the Microprocessor. It's unclear from the schematic exactly how that works, but here's what I think might be happening.
It appears that the Power Switch is a momentary pushbutton. When you press the power switch, that turns on Q3, which grounds the /PWRON line (and goes to the gate of Q2 on the RF board. That applies power to the radio, including the microprocessor. The microprocessor then asserts the POWERHOLDON signal, which turns on Q2 on the front panel PCB. That keeps the /PWRON line grounded when you release the power button. A second push of the power switch sends a different signal to the microprocessor to shut the radio down.
So, the bottom line is this: In order for the radio to turn on and stay on, Q2, Q3, and the microprocessor on the front panel PCB all have to work, as well as Q2 on the RF board. Looking at the gate of Q2 on the RF board, press and hold the power switch and see if the gate goes to ground. If so, power will come on on the RF board. Then see if the gate remains grounded when you release the power switch.
My guess, since you have been able to communicate with the microprocessor, is that the circuitry on the front panel PCB is ok and your issue is a bad Q2 on the RF board.