It sounds like a couple things to me are likely, one could be just a
stuck key. Usually if it is, it's the one that repeats when you hit
CTRL-Reset.
but since you are not seeing a repeat key until you hit something, and
that key repeats.. one of the characteristics is when you have a
stuck key, the next key you type will assume the role and be the one
echoed on the screen. Of course, the stuck key could be the control
key.. which would produce no result on screen. Or another modifier
key.
Try hitting just reset on power up, if it resets, then control is
stuck. Or.. when you hit control-Reset, hit G next. .. though, wait,
that might also produce some interesting results, and since you say
other keys are working. Nothing should work as a visible ASCII
character on screen with control pressed.
But since you are also saying some don't work at all.. that means to
me possibly the matrix has a hole in it.
So .. either the keyboard itself, or the AY-3600-Pro.
I have several extras of those, too. Hopefully it's one that is not
soldered. ..and if it's not soldered, perhaps you can just yank and
insert the thing.
The keyboard PCB is very simple otherwise.