Have you checked to see if the buttons work themselves?
DO you have a multimeter (DMM)? If not, go get one.
https://www.sparkfun.com/products/12966That's a decent cheap one.
If you do have a multimeter put it on continuity test or resistance and just put the leads on each side of the button and push the button down to see if the switch works, do this with the power off of course.
If the switch looks good, do the coin switches work? If the game is in freeplay, put it back into normal coin operation and test the coin switches. If they work then you need to start looking at the wiring to the switches, if they don't work you might have a bad IC on the PCB.