Charlie, about the red-or-green-or-broken question. I can light the red, green or nothing at all if I wish (which is possible in this application).

I am powering only one pin at a time. Due to the interconnections on the matrix, applying power to more than one pin will have undesired results.

Pass 1:
"1" on pin 1, "0" on pin 2, Input remaining pins lights the top left red LED.

Pass 2:
"1" on pin 4, "0" on pin 3, Input remaining pins lights the top green LED between pins 3 and 4.

But...

Pass 3:
"1" on pin 1, "0" on pin 2,
"1" on pin 4, "0" on pin 3, Input remaining pins lights the top left red LED and the top green LED between pins 3 and 4,
but it also lights
a red LED between pins 1 and 3 and
a green LED between pins 4 and 2
since those circuits are also completed unintentionally.

Robert