The page with a few keyboards is not an exhaustive list of keyboards that will work with the VT100 emulator. It was actually meant to just be a list of mechanical, or "retro-looking" keyboards. The truth is most basic USB keyboards will work with the emulator. Just as long as it does not have an internal USB hub.
There is very little circuitry between the PIC32 microcontroller and the USB jack. There is only a single resistor (the 4.7k). I have attached the schematic diagram. Check for 5v on pin 1 of the USB connector, then check for continuity on pin 4 to ground, pin 2 to pin 22 of the PIC 32, pin 3 to one end of the 4.7k resistor, and the other end of the resistor to pin 15 of the PIC32.
Then check continuity from the VT100 emulator board to the connection point on the main circuit board (5v, 3.3v, D18, D19, and GND). Also check for cross-continuity on the six pins for the six-pin ribbon cable connector, in case there is some hidden solder bridge under the six-pin connector to the VT100 circuit board.
Based on your description of behavior, I would be strongly suspect of the 5v line (since it has one purpose - to power the USB keyboard), or the D18/D19 lines.
I would not spend any time messing with PS/2 keyboards.