Depending on when the games were manufactured, there are lots of different connectors and, more importantly, pinouts (e.g. two games could use a 36-pin connector, but have completely different pinouts).
In the mid-80s, the
JAMMA standard was created to simplify the conversion of cabinets.
Pics might be helpful, as would be a description of what the game boards are (or pics of the gameboards if you don't know what they are).