The keyboard cable was installed backwards on the keyboard logic board. Installing it correctly brought some life to it (power light and reset key now work) but every key I press results in a dash appearing on the screen. So something is still not working.
I checked the outputs of the U1 and U4 (NAND gates) and the outputs of each gate agree with the inputs (at least the state they were in at the time, I did not pull the chips and perform a full combination test of inputs to output) and I think they're OK. U3, the 555 timer chip, does not appear to be outputting the 10Hz clock signal so it may be bad (I tested with U5 installed and removed). However, I do not feel this is the problem as it appears to be an isolated circuit providing a clock for the repeat key.
Next step is to swap out U5, the keyboard decoder, with one from my Apple II Plus (assuming the Plus keyboard has one. I figure it's easier than scoping out U5. I am also considering that the -12 volts may have been sent back through the keyboard cable and possibly damaged chips on the logic board. If replacing U5 doesn't address the problem that's where I'll look next.
The good news is it appears the keys themselves are all OK. The print a dash on the screen when pressed so that suggests they're operating properly. But I won't be able to confirm until I've solved the keyboard issue.
EDIT: The Apple II Plus keyboard is different from the Apple II keyboard and does not contain 5740 keyboard encoder so I won't be able to troubleshoot by swapping this part.