My main comment is that leaping to conclusions based on measurements of the resistance of semiconductors using a meter is not reliable because the voltage drop across diode junctions will give incorrect resistance measurements.? This makes many of your conclusions unsafe.
For example you concluded that the processor was faulty based on a resistance measurement, then powered it on and it worked.
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The problem with the unit not fully turning off could be some fault in the power control circuit, I have this and haven't got round to working out what the problem is but would look at the two FETs that do the switching and the control of the linear regulator.? Measure voltages rather than resistances.
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Take care not to short pins, sending 12V into the processor could make your predictions come true.
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Chris
