A closer read of the downloadable manual for the card (RTFM) gave the answer. The card can be accessed via the serial port in the UPS using the APC 0024C serial cable and Hyperterminal in Windows 2000.
Just quit all processes using the COM1 port, connect the PC to the UPS using the 0024C cable, launch Windows Hyperterminal, press Return, press the Reset button on the card, press Return again and enter apc in the displayed user name and password fields.
The resultant display shows the set IP address, MAC address, etc., and offers ways to change the settings.
The card is now running beautifully.