the green wires are just for the grounds. All metal parts on the jukebox should have a green wire grounding them just in case of an electrical fault. that way you don't end up with metal parts with deadly mains voltage on them.
looks like someone indeed robbed the mechanism control board out of it. without knowing more it's hard to say what else might be wrong with it.
replacing the control board is a huge step in the right direction and for sure won't work without it....install the board, power it up, then go from there.