What DNC software are you using? Can you set the handshaking to "XON/XOFF" or "DC Codes" or if those don't work, "None"
The Predator setup info on the Fanuc 3 shows a different cable (see attached). It has 4 (RTS) & 5 (CTS) tied together on the Fanuc end instead of 5 (CTS) to 7 (RTS) as in the diagram posted earlier.