If this game will not coin up then I would check your connections and the resistors mentioned earlier. Usually the manual will have the pin outs for the boards. Check them to see if there is a diffrence between the 2 bds and 4 bds. The coin up issue should be an easy fix. I would suspect that if this works with you 2 board system and does not work with your 4 board system the pin outs are probably diffrent. Like I said I have no expierence with these boards and have not looked up the manual as I am on dial up and it takes a long time to get one manual.
I would start with the coin up issue as this is usually a ground to one of the pins on the main connector. On my Galaga boards, I just put ground to one of the pins on the 44 pin connector. Same with movement, player start, and fire controlls.