I just wanted to increase the button sensitivity, and yeah that's what I think should help the system work even if the buttons are sufficiently old to be called "worn out"
(Sorry for my informal speech here, but that's just what had gone wrong with my LCD Shield - I hadn't been able to take it out for two years or so, and hence the buttons didn't seem to respond. Earlier I had captured the correct analog values of the A0 pin on pressing each button, so yeah due to the button getting worn out with age, the values must have changed. This general change in code, if I'm not mistaken, should help your button system work a long as possible).