Sorry, I came down with my first cold/flu/whatever sickness in about 4 years and had to disappear into bed.
I believe the issue was directly related to the Super I/O chip. When I went to solder the new chip on, I ensured that each pin was touching the solder pad by verifying connectivity on the ISA slot. However, for one or two pins, the slightest pressure of the multimeter probe on the Super I/O pins was causing it to make contact, even though there was no visible deflection in the pins. This was very difficult to troubleshoot. But alas, it is working fine now with the Super I/O replacement. I'm glad I did not remove the serial IC or replace the southbridge. The serial ports also work fine now.
I will probably go around to my stack of 486 motherboards and replace the Super I/O or serial IC's for those which are defective.
If a Super I/O can spontaneously fail like that, I assume many other IC's can as well.
Plan your life wisely, you'll be dead before you know it.