So it's mater of joining the SATA cable to the end of the Molex, as simple as that?
Coming out of the power supply is a SATA power cable like this.
Connect that to the left side of this splitter cable.
Splice either the 5v or 12v wires from the upper right connector to the coin door lights.
Connect the splitter's bottom right Molex to the Ultimate I/O LED power cable. (center top)
With that, you now have power to the coin door lights and LED power to the Ultimate I/O board.
Each RGB LED button will also need these 4 wires: + (operating voltage provided by the power chain above), Red ground channel, Green ground channel, and Blue ground channel.
Scott