Sounds like something is wrong with the chips in the controller. For two button game pads, there's a line switching chip and a turbo fire chip (unless it's the original non turbo pce gamepad). The chips are off the shelf parts, just make sure you get the replacement kind (if it's an HC chip or such, get the HC series part).
IIRC, the 74xx157 chip is the line select (outputs either start/select/II/I or Up/Down/Left/Right). The 74xx163 is the auto fire chip. Sounds like the problem is with the '157 chip.