So, based on the discussion, I dug out some 50-pin ribbon cable,
fastened on four connectors, and tried my KA630 with three 4M boards.
And....

+----------------
| Performing normal system tests.
| 
|   7..6..5..4..3..
| ?6 
| Failure.
| 
| Normal operation not possible.
+----------------

Except....

Unplugging the private bus cable from the last board of RAM (slot 4)
makes it pass POST (presumably with only 9MB, though I didn't verify).
And switching it around so board 3 is using private-bus connector 4,
with private-bus connector 3 disconnected, it works again.

And swapping out the board from slot 3, moving the board from slot 4 to
slot 3, and putting my other 4M board in slot 4, I see the same
behaviour.

Thus, it's not the cable, connector, or board.

What failure does "?6" indicate?

Are you _sure_ the KA630 is supposed to work with three boards of RAM?
Maybe it depends on board rev or ROM rev?  Mine shows "KA630-A.V1.2" at
power-up; I don't see anything on the board that looks obviously like a
hardware rev number.  It has a barcode sticker with printing
"*WF535F9902*", and on each side, in etch-trace text, is 5016523 01 E1.
Stamped into the metal back-edge stiffener is "M7606 AC".

It doesn't seem to indicate anything fried, either; as I mentioned
above, using two boards of memory works, even with my cable.  (I
haven't tried using two boards of memory in slots other than 2 and 3.)

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