...
During assembly, there existed many shorts on the connector for the microcontroller. I was unable to find any on the pins shorted on the micro while debugging, but it should be looked into once again if short-like problems still persist.
Conclusions
I tested again by checking if 3V actually reaches the input pins of the micro when pressed. I found that it does and the logic is inverted due to the inverted Schmitt trigger, though the 3V still reaches the micro. It is now a firmware problem.