[SiriusHardware]

Thanks for the more precise breakdown of keys pressed and characters returned. I obviously didn't completely understand which keys you had pressed and in what order originally, so the clarification / corrected table is helpful.

As you aren't keen to try to remove the 74LS145 (yet), there are other avenues to explore first but they may eventually lead you back to the 74LS145.

Can we ask what you feel your technical 'level' is - don't want to insult you by aiming advice at too low a level or confuse you by aiming too high. What do you have in the way of test and repair gear and tools?

-Soldering and desoldering tools?
-Multimeter?
-Logic Probe?
-Oscilloscope?
-Any other microprocessor items which could be pressed into diagnostic service, such as an Arduino?

While you ponder that, one thing you could try is the 8-bit Guy's trick of unplugging the keyboard and using a wire link to connect one of the row pins on the mainboard's keyboard connector to each column pin in succession.

If that gives you a nice progression of successive letters in the same order as on the keyboard row without repeating any or missing any out, that would suggest that the main board is OK and focus attention on the keyboard.