and there are 100k resistors to limit current to the board.
No there is nothing to limit the current through the LEDs.
Using common emitters circuit to drive the rows is silly, you will never get a voltage of greater than 4.3V. You need a PNP top level switch.
I was hoping to Direct Drive the matrix as seen here.Arduino Playground - HomePage
Bad tutorial that exceeds current limits on the arduino.
The letters are also upside down
Just the way you wired it up / defined the arrays.