You can test if the problem is with the control board or the plastic circuits.
Disconnect the plastic circuits from the control board, like you did in this picture:
Connect the control board to your computer and open a program (Notepad, TextEdit, etc.) so you can see if the keyboard can send letters.
Using a short piece of wire (or a paperclip) connect one of the contacts labeled R0-R17 to one of the contacts labled C0-C7.
This is like pressing the buttons on the keyboard.
Repeat this until you find the combination that produces "q" or "1".
If you still get "qi", "iq", "18" or "81", then your control board is broken.
If, using this method, you can make it just type "q" or "1", then the problem is with the plastic circuits.