oh, you're right Loopey, I must have glazed over that part.
the inputs are handled by IC chips (74LS541 octal buffer and line driver) that pass the floating/low state of the input to the CPU, there may be some schmutz on or near the IC that handles the fly-by button input. something damp or sticky on the pins could cause the input to go low and read as being activated.
check all the IC's resistors,capacitors diodes between the IC's and the JAMMA connection and make sure it is free of spills.
otherwise, you'll need to replace the buffer IC.
if searching ebay or calling around for parts... search for "74LS541 SOIC" or "SN74LS542DW" you want the surface mounted SOIC version not the PDIP package.
in a pinch you could mount a PDIP in some veroboard and use some thin ribbon cable to solder onto the pads...the pinout layout is the same...just way smaller. it's not pretty but it can work.