I've measured the connectivity, but it only confirms what I already suspected.
The points probed were, VCC & VSS in each socket, VCC & VSS on the cache module, and around the chipset.
As already said, the "Celebris Pentium PC" manual says, "Also, do not remove the external cache module. Removing the external cache module prevents the computer from operating correctly." Without the 3.3V regulator, the 3.3V cache won't get any power, so that explains why it won't POST. I still haven't been able to find a 5V cache module.
I also finished building an open frame case.