It doesn't look like you are using
https://docs.arduino.cc/libraries/keypad/
Which is used here
and should let you test with just a single jumper shorting a row and a column to simulate a key press.
That is to say use a pre-rolled algorithm, lose the little keyboard for the moment until you get the code working, which it just should.
Then worry about one real row and column (one button) om the keypad.
Then add rows and columns testing the newly included buttons with each addition.
HTH hope I read your current circumstances right.
a7