Thank you for the suggestions, torrentg. I changed the CMOS display setting (it is the most recent BIOS firmware from Dell for this E510, version A07) from 'Auto' to 'Onboard/PEG' (PCI-E Graphics will override the onboard graphics), plugged in the VGA card in a different slot.
Now under Device Manager, there is a VGA driver installed (and checking online for updates it is the latest one recommended to use according to the message box), this time with an exclamation point and 'This device cannot start. (Code 10)' under Properties. Win+P gives me the option to 'Extend Monitor' but it doesn't bring the third monitor alive.
stormy3, checking it it does happen to be also an ATI RageXL PCI card, dated year 2000. I don't even remember where I got it from...
For what its worth, the Sapphire Radeon 4670 card has a third HDMI output - do you think an HDMI -> DVI adapter would be able to drive a third monitor from the same card? I see that these adapters are $15 or so - it may be worth it for me to try it. Any feedback is welcome.