A null modem cable reverses the TX and RX connections. If the device expect a null modem cable, then this might be your problem.
Try using a serial console program like
PuTTY to communicate directly with it. Assuming it's SCPI compatible, *IDN? should return the model number and serial. Also check the settings on the DMM, you can probably switch between RS-232 and GPIB (if available) and set baud rate and other serial parameters.