As Clive has said serial can work with just the 3 wires BUT it all depends on what is sending the signals and what is receiving them as to what connections are needed.
Does your Denford machine have a 25 pin input or as you alluded to a 9 pin to 9 pin lead has it a 9 pin input.
As you are finding out the whole rs232 saga is one of trial and error, in the past when I was involved with such things I collected a selection of leads and adaptors just so that you could get the 2 parts to communicate with each other - then you could get a lead or make one.
I was never sure whether the manufacturer tried to keep things secret or they just didn't know themselves!

These days things are much easier now that the rs232 has gone (mostly) by the way.

Just as a thought have you checked the controller PC that it has the right port enabled as some require them to be enabled in the bios(if memory serves)


Peter