Try replacing the following on the game board.
R2, R18, C2
Or
R7,R23,C7
Then try U1 or U2.
(The or comes from the fact that the schematics call for Left and Right player inputs, I don't which one is player 1.)
Resistors R2 and R7 are 220ohm.
Resistors R18 and R23 are 27Kohm.
Caps are .1mfd
U1 and U2 appear to be MC14539B chips.
(Dual 4-Channel Data Selector/Multiplexer)
After these components the inputs share common lines/components.
One of those should fix the problem.
Later,
dabone