The control should be toggling the CTS (Clear To Send) signal on pin 5 of the 25 pin connector on the CNC side. In other words, when you press the key to load a program and the display says 'Busy Loading,' this is when the CTS signal should go from low to high, indicating the control is ready to receive data. I don't have my documentation with me, so this signal may jump high just entering the Load mode, but at any rate. If the CTS signal is high and the control says 'Busy Loading,' the control is "listening" to the receive line.
Hyperterminal should automatically display text as it is sending. One trick is to pull the connector off the computer end and send the file with nothing connected. If you see text scrolling, then you've got the program nominally set up correctly. If, when reconnected, you can't get the text to scroll up sending, then the CTS signal isn't being seen by the computer. To just load programs, you could jumper CTS to RTS (Request to Send) - pin 5 on the DynaPath to RTS on the computer. RTS should be on pin 7 on a 9 pin connector.
BTW, how many pins on your connector on the computer side? Usually computers have 9-pin serial ports. 25-pin connectors on a computer are usually a printer port, which is parallel. Only very early computers (usually desktops) had 25-pin serial ports.
Once you get hyperterminal scrolling and CTS high, if the control still says just 'Busy Loading,' you've probably got a blown receive line on the hardware. You wouldn't be the first.