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I removed the CPU and display boards from the case, and cleaned up the goo left by some foam between the keyboard’s keys.
Wires for providing power added:
GND black
+5v Red
+20VFX brown
+5VFX UNreg (connected to R110 1ohm then to large cap C110 +)
I connected the CPU board to a 5V power supply and checked current consumption (around 1.6A). Nothing got hot, so I checked the CPU clock (worked) and the R/W and address lines. The CPU seems to run.
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So we do seem to have data being shifted through.
Checked U103 (Parallel → serial shift register)'s SH and CLK lines (1, 2) and data out (7) and there is very little activity on it- but there is some:
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Checked U116 pin 12 (_ENABLE_) and it has a pulse train:
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Checked Q103..Q107 (display select line drivers) and there appears to be no data on the bases of those transistors. I replaced a 74145 and after that things got to live:
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The board reacts to keypresses, and things can be configured 
One done, heaps to go..